Bias in GRACE estimates of ice mass change due to accompanying sea-level change

《统计学》_各章关键术语（中英⽂对照）第⼆部分各章关键术语（中英⽂对照）第1章统计学（statistics）随机性（randomness）描述统计学（descriptive statistics）推断统计学（inferential statistics）总体（population）母体（parent）(parent population）样本、⼦样（sample）调查对象总体（respondents population）有限总体（finite population）调查的理论总体（survey’s heoretical population）超总体（super population）变量（variable）数据（data）原始数据（original data）派⽣数据（derived data）定类尺度（nominal scale）定类尺度变量（nominal scale level variable）定类尺度数据（nominal scale level data）定序尺度（ordinal scale）定序尺度变量（ordinal scale level variable）定序尺度数据（ordinal scale level data）定距尺度（interval scale）定距尺度变量（interval scale level variable）定距尺度数据（interval scale level data）定⽐尺度（ratio scale）定⽐尺度变量（ratio scale level variable）定⽐尺度数据（ratio scale level data）分类变量（categorical variable）定性变量、属性变量（qualitative variable）数值变量（numerical variable）定量变量、数量变量（quantitative variable）绝对数变量（absolute number level variable）绝对数数据（absolute number level data）⽐率变量（ratio level variable）⽐率数据（ratio level data）实验数据（experimental data）调查数据（survey data）观察数据（observed data）第2章随机性（randomness）随机现象（random phenomenon）随机试验（random experiment）事件（event）基本事件（elementary event）复合事件（union of event）必然事件（certain event）不可能事件（impossible event）基本事件空间（elementary event space）互不相容事件（mutually exclusive events）统计独⽴（statistical independent）统计相依（statistical dependence）概率（probability）古典⽅法概率（classical method probability）相对频数⽅法概率（relative frequency method probability）主观⽅法概率（subjective method probability）⼏何概率（geometric probability）条件概率（conditional probability）全概率公式（formula of total probability）贝叶斯公式（Bayes’ formula）先验概率（prior probability）后验概率（posterior probability）随机变量（random variable）离散型随机变量（discrete type random variable）连续型随机变量（continuous type random variable）概率分布（probability distribution）特征数（characteristic number）位置特征数（location characteristic number）数学期望（mathematical expectation）散布特征数（scatter characteristic number）⽅差（variance）标准差（standard deviation）变异系数（variable coefficient）贝努⾥分布（Bernoulli distribution）⼆点分布（two-point distribution） 0-1分布（zero-one distribution）贝努⾥试验（Bernoulli trials）⼆项分布（binomial distribution）超⼏何分布（hyper-geometric distribution）正态分布（normal distribution）正态概率密度函数（normal probability density function）正态概率密度曲线（normal probability density curve）正态随机变量（normal random variable）卡⽅分布（chi-square distribution）F_分布（F-distribution）t_分布（t-distribution） “学⽣”⽒t_分布（Student’s t-distribution）列联表（contingency table）联合概率分布（joint probability distribution）边缘概率分布（marginal probability distribution）条件分布（conditional distribution）协⽅差（covariance）相关系数（correlation coefficient）第3章统计调查（statistical survey）数据收集（collection of data）统计单位（statistical unit）统计个体（statistical individual）社会经济总体（socioeconomic population）调查对象总体（respondents population）有限总体（finite population）标志（character）标志值（character value）属性标志（attributive character ）品质标志（qualitative character ）数量标志（numerical indication）不变标志（invariant indication）变异（variation）调查条⽬（item of survey）指标（indicator）统计指标（statistical indicator）总量指标（total amount indicator）绝对数（absolute number）统计单位总量（total amount of statistical unit ）标志值总量（total amount of indication value）（total amount of character value）时期性总量指标（time period total amount indicator）流量指标（flow indicator）时点性总量指标（time point total amount indicator）存量指标（stock indicator）平均指标（average indicator）平均数（average number）相对指标（relative indicator）相对数（relative number）动态相对指标（dynamic relative indicator）发展速度（speed of development）增长速度（speed of growth）增长量（growth amount）百分点（percentage point）计划完成相对指标（relative indicator of fulfilling plan）⽐较相对指标（comparison relative indicator）结构相对指标（structural relative indicator）强度相对指标（intensity relative indicator）基期（base period）报告期（given period）分组（classification）（grouping）统计分组（statistical classification）（statistical grouping）组（class）（group）分组设计（class divisible design）（group divisible design）互斥性（mutually exclusive）包容性（hold）分组标志（classification character）（grouping character）按品质标志分组（classification by qualitative character）（grouping by qualitative character）按数量标志分组（classification by numerical indication）（grouping by numerical indication）离散型分组标志（discrete classification character）（discrete grouping character）连续型分组标志（continuous classification character）（continuous grouping character）单项式分组设计（single-valued class divisible design）（single-valued group divisible design）组距式分组设计（class interval divisible design）（group interval divisible design）组界（class boundary）（group boundary）频数（frequency）（frequency number）频率（frequency）组距（class interval）（group interval）组限（class limit）（group limit）下限（lower limit）上限（upper limit）组中值（class mid-value）（group mid-value）开⼝组（open class）（open-end class）（open-end group）开⼝式分组（open-end grouping）等距式分组设计（equal class interval divisible design）（equal group interval divisible design）不等距分组设计（unequal class interval divisible design）（unequal group interval divisible design）调查⽅案（survey plan）抽样调查（sample survey）有限总体概率抽样（probability sampling in finite populations）抽样单位（sampling unit）个体抽样（elements sampling）等距抽样（systematic sampling）整群抽样（cluster sampling）放回抽样（sampling with replacement）不放回抽样（sampling without replacement）分层抽样（stratified sampling）概率样本（probability sample）样本统计量（sample statistic）估计量（estimator）估计值（estimate）⽆偏估计量（unbiased estimator）有偏估计量（biased estimator）偏差（bias）精度（degree of precision）估计量的⽅差（variance of estimates）标准误（standard error）准确度（degree of accuracy）均⽅误差（mean square error）估计（estimation）点估计（point estimation）区间估计（interval estimate）置信区间（confidence interval）置信下限（confidence lower limit）置信上限（confidence upper limit）置信概率（confidence probability）总体均值（population mean）总体总值（population total）总体⽐例（population proportion）总体⽐率（population ratio）简单随机抽样（simple random sampling）简单随机样本（simple random sample）研究域（domains of study）⼦总体（subpopulations）抽样框（frame）估计量的估计⽅差（estimated variance of estimates）第4章频数（frequency）（frequency number）频率（frequency）分布列（distribution series）经验分布（empirical distribution）理论分布（theoretical distribution）品质型数据分布列（qualitative data distribution series）数量型数据分布列（quantitative data distribution series）单项式数列（single-valued distribution series）组距式数列（class interval distribution series）频率密度（frequency density）分布棒图（bar graph of distribution）分布直⽅图（histogram of distribution）分布折线图（polygon of distribution）累积分布数列（cumulative distribution series）累积分布图（polygon of cumulative distribution）位置特征（location characteristic）位置特征数（location characteristic number）平均值、均值（mean）平均数（average number）权数（weight number）加权算术平均数（weighted arithmetic average）加权算术平均值（weighted arithmetic mean）简单算术平均数（simple arithmetic average）简单算术平均值（simple arithmetic mean）加权调和平均数（weighted harmonic average）加权调和平均值（weighted harmonic mean）简单调和平均数（simple harmonic average）简单调和平均值（simple harmonic mean）加权⼏何平均数（weighted geometric average）加权⼏何平均值（weighted geometric mean）简单⼏何平均数（simple geometric average）简单⼏何平均值（simple geometric mean）绝对数数据（absolute number data）⽐率类型数据（ratio level data）中位数（median）众数（mode）耐抗性（resistance）散布特征（scatter characteristic）散布特征数（scatter characteristic number）极差、全距（range）四分位差（quartile deviation）四分间距（inter-quartile range）上四分位数（upper quartile）下四分位数（lower quartile）在外截断点（outside cutoffs）平均差（mean deviation）⽅差（variance）标准差（standard deviation）变异系数（variable coefficient）第5章随机样本（random sample）简单随机样本（simple random sample）参数估计（parameter estimation）矩（moment）矩估计（moment estimation）修正样本⽅差（modified sample variance）极⼤似然估计（maximum likelihood estimate）参数空间（space of paramete）似然函数（likelihood function）似然⽅程（likelihood equation）点估计（point estimation）区间估计（interval estimation）假设检验（test of hypothesis）原假设（null hypothesis）备择假设（alternative hypothesis）检验统计量（statistic for test）观察到的显著⽔平（observed significance level）显著性检验（test of significance）显著⽔平标准（critical of significance level）临界值（critical value）拒绝域（rejection region）接受域（acceptance region）临界值检验规则（test regulation by critical value）双尾检验（two-tailed tests）显著⽔平（significance level）单尾检验（one-tailed tests）第⼀类错误（first-kind error）第⼀类错误概率（probability of first-kind error）第⼆类错误（second-kind error）第⼆类错误概率（probability of second-kind error）P_值（P_value）P_值检验规则（test regulation by P_value）经典统计学（classical statistics）贝叶斯统计学（Bayesian statistics）第6章⽅差分析（analysis of variance，ANOVA）⽅差分析恒等式（analysis of variance identity equation）单因⼦⽅差分析（one-factor analysis of variance）双因⼦⽅差分析（two-factor analysis of variance）总变差平⽅和（total variation sum of squares）总平⽅和SST（total sum of squares）组间变差平⽅和（among class(group) variation sum of squares），回归平⽅和SSR（regression sum of squares）组内变差平⽅和（within variation sum of squares）误差平⽅和SSE（error sum ofsquares）⽪尔逊χ2统计量（Pearson’s chi-statistic）分布拟合（fitting of distrbution）分布拟合检验（test of fitting of distrbution）⽪尔逊χ2检验（Pearson’s chi-square test）列联表（contingency table）独⽴性检验（test of independence）数量变量（quantitative variable）属性变量（qualitative variable）对数线性模型（loglinear model）回归分析（regression analysis）随机项（random term）随机扰动项（random disturbance term）回归系数（regression coefficient）总体⼀元线性回归模型（population linear regression model with a single regressor）总体多元线性回归模型（population multiple regression model with a single regressor）完全多重共线性（perfect multicollinearity）遗漏变量（omitted variable）遗漏变量偏差（omitted variable bias）⾯板数据（panel data）⾯板数据回归（panel data regressions）⼯具变量（instrumental variable）⼯具变量回归（instrumental variable regressions）两阶段最⼩平⽅估计量（two stage least squares estimator）随机化实验（randomized experiment）准实验（quasi-experiment）⾃然实验（natural experiment）普通最⼩平⽅准则（ordinary least squares criterion）最⼩平⽅准则（least squares criterion）普通最⼩平⽅（ordinary least squares，OLS）最⼩平⽅（least squares）最⼩平⽅法（least squares method）第7章简单总体（simple population）复合总体（combined population）个体指数：价⽐（price relative），量⽐（quantity relative）总指数（general index）（combined index）统计指数（statistical indices）类指数、组指数（class index）动态指数（dynamic index）⽐较指数（comparison index）计划完成指数（index of fulfilling plan）数量指标指数（quantitative indicator index）物量指数（quantitative index）（quantity index）（quantum index）质量指标指数（qualitative indicator index）价格指数、物价指数（price index）综合指数（aggregative index）（composite index）拉斯贝尔指数（Laspeyres’ index）派许指数（Paasche’s index）阿斯·杨指数（Arthur Young’s index）马歇尔—埃奇沃斯指数（Marshall-Edgeworth’s index）理想指数（ideal index）加权综合指数（weighted aggregate index）平均指数（average index）加权算术平均指数（weighted arithmetic average index）加权调和平均指数（weighted harmonic average index）因⼦互换（factor-reversal）购买⼒平价（purchasing power parity，PPP）环⽐指数（chain index）定基指数（fixed base index）连环替代因素分析法（factor analysis by chain substitution method）不变结构指数、固定构成指数（index of invariable construction）结构指数、结构影响指数（structural index）第8章截⾯数据（cross-section data）时序数据（time series data）动态数据（dynamic data）时间数列（time series）发展⽔平（level of development）基期⽔平（level of base period）报告期⽔平（level of given period）平均发展⽔平（average level of development）序时平均数（chronological average）增长量（growth quantity）平均增长量（average growth amount）发展速度（speed of development）增长速度（speed of growth）增长率（growth rate）环⽐发展速度（chained speed of development）定基发展速度（fixed base speed of development）环⽐增长速度（chained growth speed）定基增长速度（fixed base growth speed）平均发展速度（average speed of development）平均增长速度（average speed of growth）平均增长率（average growth rate）算术图（arithmetic chart）半对数图（semilog graph）时间数列散点图（scatter diagram of time series）时间数列折线图（broken line graph of time series）⽔平型时间数列（horizontal patterns in time series data）趋势型时间数列（trend patterns in time series data）季节型时间数列（season patterns in time series data）趋势—季节型时间数列（trend-season patterns in time series data）⼀次指数平滑平均数（simple exponential smoothing mean）⼀次指数平滑法（simple exponential smoothing method）最⼩平⽅法（leas square method）最⼩平⽅准则（least squares criterion）原资料平均法（average of original data method）季节模型（seasonal model）（seasonal pattern）长期趋势（secular trends）季节变动（变差）（seasonal variation）季节波动（seasonal fluctuations）不规则变动（变差）（erratic variation）不规则波动（random fluctuations）时间数列加法模型（additive model of time series）时间数列乘法模型（multiplicative model of time series）。

CHAPTER 13TEACHING NOTESWhile this chapter falls under “Advanced Topics,” most of this chapter requires no more sophistication than the previous chapters. (In fact, I would argue that, with the possible exception of Section 13.5, this material is easier than some of the time series chapters.)Pooling two or more independent cross sections is a straightforward extension of cross-sectional methods. Nothing new needs to be done in stating assumptions, except possibly mentioning that random sampling in each time period is sufficient. The practically important issue is allowing for different intercepts, and possibly different slopes, across time.The natural experiment material and extensions of the difference-in-differences estimator is widely applicable and, with the aid of the examples, easy to understand.Two years of panel data are often available, in which case differencing across time is a simple way of removing g unobserved heterogeneity. If you have covered Chapter 9, you might compare this with a regression in levels using the second year of data, but where a lagged dependent variable is included. (The second approach only requires collecting information on the dependent variable in a previous year.) These often give similar answers. Two years of panel data, collected before and after a policy change, can be very powerful for policy analysis. Having more than two periods of panel data causes slight complications in that the errors in the differenced equation may be serially correlated. (However, the traditional assumption that the errors in the original equation are serially uncorrelated is not always a good one. In other words, it is not always more appropriate to used fixed effects, as in Chapter 14, than first differencing.) With large N and relatively small T, a simple way to account for possible serial correlation after differencing is to compute standard errors that are robust to arbitrary serial correlation and heteroskedasticity. Econometrics packages that do cluster analysis (such as Stata) often allow this by specifying each cross-sectional unit as its own cluster.108SOLUTIONS TO PROBLEMS13.1 Without changes in the averages of any explanatory variables, the average fertility rate fellby .545 between 1972 and 1984; this is simply the coefficient on y84. To account for theincrease in average education levels, we obtain an additional effect: –.128(13.3 – 12.2) ≈–.141. So the drop in average fertility if the average education level increased by 1.1 is .545+ .141 = .686, or roughly two-thirds of a child per woman.13.2 The first equation omits the 1981 year dummy variable, y81, and so does not allow anyappreciation in nominal housing prices over the three year period in the absence of an incinerator. The interaction term in this case is simply picking up the fact that even homes that are near the incinerator site have appreciated in value over the three years. This equation suffers from omitted variable bias.The second equation omits the dummy variable for being near the incinerator site, nearinc,which means it does not allow for systematic differences in homes near and far from the sitebefore the site was built. If, as seems to be the case, the incinerator was located closer to lessvaluable homes, then omitting nearinc attributes lower housing prices too much to theincinerator effect. Again, we have an omitted variable problem. This is why equation (13.9) (or,even better, the equation that adds a full set of controls), is preferred.13.3 We do not have repeated observations on the same cross-sectional units in each time period,and so it makes no sense to look for pairs to difference. For example, in Example 13.1, it is veryunlikely that the same woman appears in more than one year, as new random samples areobtained in each year. In Example 13.3, some houses may appear in the sample for both 1978and 1981, but the overlap is usually too small to do a true panel data analysis.β, but only13.4 The sign of β1 does not affect the direction of bias in the OLS estimator of1whether we underestimate or overestimate the effect of interest. If we write ∆crmrte i = δ0 +β1∆unem i + ∆u i, where ∆u i and ∆unem i are negatively correlated, then there is a downward biasin the OLS estimator of β1. Because β1 > 0, we will tend to underestimate the effect of unemployment on crime.13.5 No, we cannot include age as an explanatory variable in the original model. Each person inthe panel data set is exactly two years older on January 31, 1992 than on January 31, 1990. This means that ∆age i = 2 for all i. But the equation we would estimate is of the form∆saving i = δ0 + β1∆age i +…,where δ0 is the coefficient the year dummy for 1992 in the original model. As we know, whenwe have an intercept in the model we cannot include an explanatory variable that is constant across i; this violates Assumption MLR.3. Intuitively, since age changes by the same amount for everyone, we cannot distinguish the effect of age from the aggregate time effect.10913.6 (i) Let FL be a binary variable equal to one if a person lives in Florida, and zero otherwise. Let y90 be a year dummy variable for 1990. Then, from equation (13.10), we have the linear probability modelarrest = β0 + δ0y90 + β1FL + δ1y90⋅FL + u.The effect of the law is measured by δ1, which is the change in the probability of drunk driving arrest due to the new law in Florida. Including y90 allows for aggregate trends in drunk driving arrests that would affect both states; including FL allows for systematic differences between Florida and Georgia in either drunk driving behavior or law enforcement.(ii) It could be that the populations of drivers in the two states change in different ways over time. For example, age, race, or gender distributions may have changed. The levels of education across the two states may have changed. As these factors might affect whether someone is arrested for drunk driving, it could be important to control for them. At a minimum, there is the possibility of obtaining a more precise estimator of δ1 by reducing the error variance. Essentially, any explanatory variable that affects arrest can be used for this purpose. (See Section 6.3 for discussion.)SOLUTIONS TO COMPUTER EXERCISES13.7 (i) The F statistic (with 4 and 1,111 df) is about 1.16 and p-value ≈ .328, which shows that the living environment variables are jointly insignificant.(ii) The F statistic (with 3 and 1,111 df) is about 3.01 and p-value ≈ .029, and so the region dummy variables are jointly significant at the 5% level.(iii) After obtaining the OLS residuals, ˆu, from estimating the model in Table 13.1, we run the regression 2ˆu on y74, y76, …, y84 using all 1,129 observations. The null hypothesis of homoskedasticity is H0: γ1 = 0, γ2= 0, … , γ6 = 0. So we just use the usual F statistic for joint significance of the year dummies. The R-squared is about .0153 and F ≈ 2.90; with 6 and 1,122 df, the p-value is about .0082. So there is evidence of heteroskedasticity that is a function of time at the 1% significance level. This suggests that, at a minimum, we should compute heteroskedasticity-robust standard errors, t statistics, and F statistics. We could also use weighted least squares (although the form of heteroskedasticity used here may not be sufficient; it does not depend on educ, age, and so on).(iv) Adding y74⋅educ, , y84⋅educ allows the relationship between fertility and education to be different in each year; remember, the coefficient on the interaction gets added to the coefficient on educ to get the slope for the appropriate year. When these interaction terms are added to the equation, R2≈ .137. The F statistic for joint significance (with 6 and 1,105 df) is about 1.48 with p-value ≈ .18. Thus, the interactions are not jointly significant at even the 10% level. This is a bit misleading, however. An abbreviated equation (which just shows the coefficients on the terms involving educ) is110111kids= -8.48 - .023 educ + - .056 y74⋅educ - .092 y76⋅educ(3.13) (.054) (.073) (.071) - .152 y78⋅educ - .098 y80⋅educ - .139 y82⋅educ - .176 y84⋅educ .(.075) (.070) (.068) (.070)Three of the interaction terms, y78⋅educ , y82⋅educ , and y84⋅educ are statistically significant at the 5% level against a two-sided alternative, with the p -value on the latter being about .012. The coefficients are large in magnitude as well. The coefficient on educ – which is for the base year, 1972 – is small and insignificant, suggesting little if any relationship between fertility andeducation in the early seventies. The estimates above are consistent with fertility becoming more linked to education as the years pass. The F statistic is insignificant because we are testing some insignificant coefficients along with some significant ones.13.8 (i) The coefficient on y85 is roughly the proportionate change in wage for a male (female = 0) with zero years of education (educ = 0). This is not especially useful since we are not interested in people with no education.(ii) What we want to estimate is θ0 = δ0 + 12δ1; this is the change in the intercept for a male with 12 years of education, where we also hold other factors fixed. If we write δ0 = θ0 - 12δ1, plug this into (13.1), and rearrange, we getlog(wage ) = β0 + θ0y85 + β1educ + δ1y85⋅(educ – 12) + β2exper + β3exper 2 + β4union + β5female + δ5y85⋅female + u .Therefore, we simply replace y85⋅educ with y85⋅(educ – 12), and then the coefficient andstandard error we want is on y85. These turn out to be 0ˆθ = .339 and se(0ˆθ) = .034. Roughly, the nominal increase in wage is 33.9%, and the 95% confidence interval is 33.9 ± 1.96(3.4), or about 27.2% to 40.6%. (Because the proportionate change is large, we could use equation (7.10), which implies the point estimate 40.4%; but obtaining the standard error of this estimate is harder.)(iii) Only the coefficient on y85 differs from equation (13.2). The new coefficient is about –.383 (se ≈ .124). This shows that real wages have fallen over the seven year period, although less so for the more educated. For example, the proportionate change for a male with 12 years of education is –.383 + .0185(12) = -.161, or a fall of about 16.1%. For a male with 20 years of education there has been almost no change [–.383 + .0185(20) = –.013].(iv) The R -squared when log(rwage ) is the dependent variable is .356, as compared with .426 when log(wage ) is the dependent variable. If the SSRs from the regressions are the same, but the R -squareds are not, then the total sum of squares must be different. This is the case, as the dependent variables in the two equations are different.(v) In 1978, about 30.6% of workers in the sample belonged to a union. In 1985, only about 18% belonged to a union. Therefore, over the seven-year period, there was a notable fall in union membership.(vi) When y85⋅union is added to the equation, its coefficient and standard error are about -.00040 (se ≈ .06104). This is practically very small and the t statistic is almost zero. There has been no change in the union wage premium over time.(vii) Parts (v) and (vi) are not at odds. They imply that while the economic return to union membership has not changed (assuming we think we have estimated a causal effect), the fraction of people reaping those benefits has fallen.13.9 (i) Other things equal, homes farther from the incinerator should be worth more, so δ1 > 0. If β1 > 0, then the incinerator was located farther away from more expensive homes.(ii) The estimated equation islog()price= 8.06 -.011 y81+ .317 log(dist) + .048 y81⋅log(dist)(0.51) (.805) (.052) (.082)n = 321, R2 = .396, 2R = .390.ˆδ = .048 is the expected sign, it is not statistically significant (t statistic ≈ .59).While1(iii) When we add the list of housing characteristics to the regression, the coefficient ony81⋅log(dist) becomes .062 (se = .050). So the estimated effect is larger – the elasticity of price with respect to dist is .062 after the incinerator site was chosen – but its t statistic is only 1.24. The p-value for the one-sided alternative H1: δ1 > 0 is about .108, which is close to being significant at the 10% level.13.10 (i) In addition to male and married, we add the variables head, neck, upextr, trunk, lowback, lowextr, and occdis for injury type, and manuf and construc for industry. The coefficient on afchnge⋅highearn becomes .231 (se ≈ .070), and so the estimated effect and t statistic are now larger than when we omitted the control variables. The estimate .231 implies a substantial response of durat to the change in the cap for high-earnings workers.(ii) The R-squared is about .041, which means we are explaining only a 4.1% of the variation in log(durat). This means that there are some very important factors that affect log(durat) that we are not controlling for. While this means that predicting log(durat) would be very difficultˆδ: it could still for a particular individual, it does not mean that there is anything biased about1be an unbiased estimator of the causal effect of changing the earnings cap for workers’ compensation.(iii) The estimated equation using the Michigan data is112durat= 1.413 + .097 afchnge+ .169 highearn+ .192 afchnge⋅highearn log()(0.057) (.085) (.106) (.154)n = 1,524, R2 = .012.The estimate of δ1, .192, is remarkably close to the estimate obtained for Kentucky (.191). However, the standard error for the Michigan estimate is much higher (.154 compared with .069). The estimate for Michigan is not statistically significant at even the 10% level against δ1 > 0. Even though we have over 1,500 observations, we cannot get a very precise estimate. (For Kentucky, we have over 5,600 observations.)13.11 (i) Using pooled OLS we obtainrent= -.569 + .262 d90+ .041 log(pop) + .571 log(avginc) + .0050 pctstu log()(.535) (.035) (.023) (.053) (.0010) n = 128, R2 = .861.The positive and very significant coefficient on d90 simply means that, other things in the equation fixed, nominal rents grew by over 26% over the 10 year period. The coefficient on pctstu means that a one percentage point increase in pctstu increases rent by half a percent (.5%). The t statistic of five shows that, at least based on the usual analysis, pctstu is very statistically significant.(ii) The standard errors from part (i) are not valid, unless we thing a i does not really appear in the equation. If a i is in the error term, the errors across the two time periods for each city are positively correlated, and this invalidates the usual OLS standard errors and t statistics.(iii) The equation estimated in differences islog()∆= .386 + .072 ∆log(pop) + .310 log(avginc) + .0112 ∆pctsturent(.037) (.088) (.066) (.0041)n = 64, R2 = .322.Interestingly, the effect of pctstu is over twice as large as we estimated in the pooled OLS equation. Now, a one percentage point increase in pctstu is estimated to increase rental rates by about 1.1%. Not surprisingly, we obtain a much less precise estimate when we difference (although the OLS standard errors from part (i) are likely to be much too small because of the positive serial correlation in the errors within each city). While we have differenced away a i, there may be other unobservables that change over time and are correlated with ∆pctstu.(iv) The heteroskedasticity-robust standard error on ∆pctstu is about .0028, which is actually much smaller than the usual OLS standard error. This only makes pctstu even more significant (robust t statistic ≈ 4). Note that serial correlation is no longer an issue because we have no time component in the first-differenced equation.11311413.12 (i) You may use an econometrics software package that directly tests restrictions such as H 0: β1 = β2 after estimating the unrestricted model in (13.22). But, as we have seen many times, we can simply rewrite the equation to test this using any regression software. Write the differenced equation as∆log(crime ) = δ0 + β1∆clrprc -1 + β2∆clrprc -2 + ∆u .Following the hint, we define θ1 = β1 - β2, and then write β1 = θ1 + β2. Plugging this into the differenced equation and rearranging gives∆log(crime ) = δ0 + θ1∆clrprc -1 + β2(∆clrprc -1 + ∆clrprc -2) + ∆u .Estimating this equation by OLS gives 1ˆθ= .0091, se(1ˆθ) = .0085. The t statistic for H 0: β1 = β2 is .0091/.0085 ≈ 1.07, which is not statistically significant.(ii) With β1 = β2 the equation becomes (without the i subscript)∆log(crime ) = δ0 + β1(∆clrprc -1 + ∆clrprc -2) + ∆u= δ0 + δ1[(∆clrprc -1 + ∆clrprc -2)/2] + ∆u ,where δ1 = 2β1. But (∆clrprc -1 + ∆clrprc -2)/2 = ∆avgclr .(iii) The estimated equation islog()crime ∆ = .099 - .0167 ∆avgclr(.063) (.0051)n = 53, R 2 = .175, 2R = .159.Since we did not reject the hypothesis in part (i), we would be justified in using the simplermodel with avgclr . Based on adjusted R -squared, we have a slightly worse fit with the restriction imposed. But this is a minor consideration. Ideally, we could get more data to determine whether the fairly different unconstrained estimates of β1 and β2 in equation (13.22) reveal true differences in β1 and β2.13.13 (i) Pooling across semesters and using OLS givestrmgpa = -1.75 -.058 spring+ .00170 sat- .0087 hsperc(0.35) (.048) (.00015) (.0010)+ .350 female- .254 black- .023 white- .035 frstsem(.052) (.123) (.117) (.076)- .00034 tothrs + 1.048 crsgpa- .027 season(.00073) (0.104) (.049)n = 732, R2 = .478, 2R = .470.The coefficient on season implies that, other things fixed, an athlete’s term GPA is about .027 points lower when his/her sport is in season. On a four point scale, this a modest effect (although it accumulates over four years of athletic eligibility). However, the estimate is not statistically significant (t statistic ≈-.55).(ii) The quick answer is that if omitted ability is correlated with season then, as we know form Chapters 3 and 5, OLS is biased and inconsistent. The fact that we are pooling across two semesters does not change that basic point.If we think harder, the direction of the bias is not clear, and this is where pooling across semesters plays a role. First, suppose we used only the fall term, when football is in season. Then the error term and season would be negatively correlated, which produces a downward bias in the OLS estimator of βseason. Because βseason is hypothesized to be negative, an OLS regression using only the fall data produces a downward biased estimator. [When just the fall data are used, ˆβ = -.116 (se = .084), which is in the direction of more bias.] However, if we use just the seasonspring semester, the bias is in the opposite direction because ability and season would be positive correlated (more academically able athletes are in season in the spring). In fact, using just theβ = .00089 (se = .06480), which is practically and statistically equal spring semester gives ˆseasonto zero. When we pool the two semesters we cannot, with a much more detailed analysis, determine which bias will dominate.(iii) The variables sat, hsperc, female, black, and white all drop out because they do not vary by semester. The intercept in the first-differenced equation is the intercept for the spring. We have∆= -.237 + .019 ∆frstsem+ .012 ∆tothrs+ 1.136 ∆crsgpa- .065 seasontrmgpa(.206) (.069) (.014) (0.119) (.043) n = 366, R2 = .208, 2R = .199.Interestingly, the in-season effect is larger now: term GPA is estimated to be about .065 points lower in a semester that the sport is in-season. The t statistic is about –1.51, which gives a one-sided p-value of about .065.115(iv) One possibility is a measure of course load. If some fraction of student-athletes take a lighter load during the season (for those sports that have a true season), then term GPAs may tend to be higher, other things equal. This would bias the results away from finding an effect of season on term GPA.13.14 (i) The estimated equation using differences is∆= -2.56 - 1.29 ∆log(inexp) - .599 ∆log(chexp) + .156 ∆incshrvote(0.63) (1.38) (.711) (.064)n = 157, R2 = .244, 2R = .229.Only ∆incshr is statistically significant at the 5% level (t statistic ≈ 2.44, p-value ≈ .016). The other two independent variables have t statistics less than one in absolute value.(ii) The F statistic (with 2 and 153 df) is about 1.51 with p-value ≈ .224. Therefore,∆log(inexp) and ∆log(chexp) are jointly insignificant at even the 20% level.(iii) The simple regression equation is∆= -2.68 + .218 ∆incshrvote(0.63) (.032)n = 157, R2 = .229, 2R = .224.This equation implies t hat a 10 percentage point increase in the incumbent’s share of total spending increases the percent of the incumbent’s vote by about 2.2 percentage points.(iv) Using the 33 elections with repeat challengers we obtain∆= -2.25 + .092 ∆incshrvote(1.00) (.085)n = 33, R2 = .037, 2R = .006.The estimated effect is notably smaller and, not surprisingly, the standard error is much larger than in part (iii). While the direction of the effect is the same, it is not statistically significant (p-value ≈ .14 against a one-sided alternative).13.15 (i) When we add the changes of the nine log wage variables to equation (13.33) we obtain116117 log()crmrte ∆ = .020 - .111 d83 - .037 d84 - .0006 d85 + .031 d86 + .039 d87(.021) (.027) (.025) (.0241) (.025) (.025)- .323 ∆log(prbarr ) - .240 ∆log(prbconv ) - .169 ∆log(prbpris )(.030) (.018) (.026)- .016 ∆log(avgsen ) + .398 ∆log(polpc ) - .044 ∆log(wcon )(.022) (.027) (.030)+ .025 ∆log(wtuc ) - .029 ∆log(wtrd ) + .0091 ∆log(wfir )(0.14) (.031) (.0212)+ .022 ∆log(wser ) - .140 ∆log(wmfg ) - .017 ∆log(wfed )(.014) (.102) (.172)- .052 ∆log(wsta ) - .031 ∆log(wloc ) (.096) (.102) n = 540, R 2 = .445, 2R = .424.The coefficients on the criminal justice variables change very modestly, and the statistical significance of each variable is also essentially unaffected.(ii) Since some signs are positive and others are negative, they cannot all really have the expected sign. For example, why is the coefficient on the wage for transportation, utilities, and communications (wtuc ) positive and marginally significant (t statistic ≈ 1.79)? Higher manufacturing wages lead to lower crime, as we might expect, but, while the estimated coefficient is by far the largest in magnitude, it is not statistically different from zero (tstatistic ≈ –1.37). The F test for joint significance of the wage variables, with 9 and 529 df , yields F ≈ 1.25 and p -value ≈ .26.13.16 (i) The estimated equation using the 1987 to 1988 and 1988 to 1989 changes, where we include a year dummy for 1989 in addition to an overall intercept, isˆhrsemp ∆ = –.740 + 5.42 d89 + 32.60 ∆grant + 2.00 ∆grant -1 + .744 ∆log(employ ) (1.942) (2.65) (2.97) (5.55) (4.868)n = 251, R 2 = .476, 2R = .467.There are 124 firms with both years of data and three firms with only one year of data used, for a total of 127 firms; 30 firms in the sample have missing information in both years and are not used at all. If we had information for all 157 firms, we would have 314 total observations in estimating the equation.(ii) The coefficient on grant – more precisely, on ∆grant in the differenced equation – means that if a firm received a grant for the current year, it trained each worker an average of 32.6 hoursmore than it would have otherwise. This is a practically large effect, and the t statistic is very large.(iii) Since a grant last year was used to pay for training last year, it is perhaps not surprising that the grant does not carry over into more training this year. It would if inertia played a role in training workers.(iv) The coefficient on the employees variable is very small: a 10% increase in employ increases hours per employee by only .074. [Recall:∆≈ (.744/100)(%∆employ).] Thishrsempis very small, and the t statistic is also rather small.13.17. (i) Take changes as usual, holding the other variables fixed: ∆math4it = β1∆log(rexpp it) = (β1/100)⋅[ 100⋅∆log(rexpp it)] ≈ (β1/100)⋅( %∆rexpp it). So, if %∆rexpp it = 10, then ∆math4it= (β1/100)⋅(10) = β1/10.(ii) The equation, estimated by pooled OLS in first differences (except for the year dummies), is4∆ = 5.95 + .52 y94 + 6.81 y95- 5.23 y96- 8.49 y97 + 8.97 y98math(.52) (.73) (.78) (.73) (.72) (.72)- 3.45 ∆log(rexpp) + .635 ∆log(enroll) + .025 ∆lunch(2.76) (1.029) (.055)n = 3,300, R2 = .208.Taken literally, the spending coefficient implies that a 10% increase in real spending per pupil decreases the math4 pass rate by about 3.45/10 ≈ .35 percentage points.(iii) When we add the lagged spending change, and drop another year, we get4∆ = 6.16 + 5.70 y95- 6.80 y96- 8.99 y97 +8.45 y98math(.55) (.77) (.79) (.74) (.74)- 1.41 ∆log(rexpp) + 11.04 ∆log(rexpp-1) + 2.14 ∆log(enroll)(3.04) (2.79) (1.18)+ .073 ∆lunch(.061)n = 2,750, R2 = .238.The contemporaneous spending variable, while still having a negative coefficient, is not at all statistically significant. The coefficient on the lagged spending variable is very statistically significant, and implies that a 10% increase in spending last year increases the math4 pass rate118119 by about 1.1 percentage points. Given the timing of the tests, a lagged effect is not surprising. In Michigan, the fourth grade math test is given in January, and so if preparation for the test begins a full year in advance, spending when the students are in third grade would at least partly matter.(iv) The heteroskedasticity-robust standard error for log() ˆrexpp β∆is about 4.28, which reducesthe significance of ∆log(rexpp ) even further. The heteroskedasticity-robust standard error of 1log() ˆrexpp β-∆is about 4.38, which substantially lowers the t statistic. Still, ∆log(rexpp -1) is statistically significant at just over the 1% significance level against a two-sided alternative.(v) The fully robust standard error for log() ˆrexpp β∆is about 4.94, which even further reducesthe t statistic for ∆log(rexpp ). The fully robust standard error for 1log() ˆrexpp β-∆is about 5.13,which gives ∆log(rexpp -1) a t statistic of about 2.15. The two-sided p -value is about .032.(vi) We can use four years of data for this test. Doing a pooled OLS regression of ,1垐 on it i t r r -,using years 1995, 1996, 1997, and 1998 gives ˆρ= -.423 (se = .019), which is strong negative serial correlation.(vii) Th e fully robust “F ” test for ∆log(enroll ) and ∆lunch , reported by Stata 7.0, is .93. With 2 and 549 df , this translates into p -value = .40. So we would be justified in dropping these variables, but they are not doing any harm.。

AbstractBackground: Whether depression causes increased risk of the development of breast cancer has long been debated. We conducted an updated meta-analysis of cohort studies to assess the association between depression and risk of breast cancer. Materials and Methods: Relevant literature was searched from Medline, Embase, Web of Science (up to April 2014) as well as manual searches of reference lists of selected publications. Cohort studies on the association between depression and breast cancer were included. Data abstraction and quality assessment were conducted independently by two authors. Random-effect model was used to compute the pooled risk estimate. Visual inspection of a funnel plot, Begg rank correlation test and Egger linear regression test were used to evaluate the publication bias. Results: We identified eleven cohort studies (182,241 participants, 2,353 cases) with a follow-up duration ranging from 5 to 38 years. The pooled adjusted RR was 1.13(95% CI: 0.94 to 1.36; I2=67.2%, p=0.001). The association between the risk of breast cancer and depression was consistent across subgroups. Visual inspection of funnel plot and Begg’s and Egger’s tests indicated no evidence of publication bias. Regarding limitations, a one-time assessment of depression with no measure of duration weakens the test of hypothesis. In addition, 8 different scales were used for the measurementof depression, potentially adding to the multiple conceptual problems concerned with the definition of depression. Conclusions: Available epidemiological evidence is insufficient to support a positive association between depression and breast cancer.IntroductionDepression is highly prevalent in the general population, and it is estimated that 5.8% of men and 9.5% of women will experience a depressive episode in a 12-month period. The lifetime incidence of depression has been estimated at more than 16% in the general population (World Health Organization, 2001; Kessler et al., 2003; World Health Organization, 2008). Breast cancer is by far the most commom cancer in women (International Agency for Research on Cancer, 2008), the global burden of breast cancer measured by incidence and mortality is substantial and on the increase (Benson et al., 2012). There are an estimated 1.5 million cases diagnosed annually and almost 0.5 million died from this disease, representing 14% of female cancer deaths in the worldwide (Jemal et al., 2011; Benson et al., 2012). Many factors have been shown to be associated with the occurrence of breast cancer, such as having a first degree relative with breast cancer, bearing the first child at a late age, alcohol consumption and long term use of menopausal estrogen replacement therapy (Kampert et al., 1988; Gail et al., 1989;Slattery et al., 1993). However, it has long been debated that whether depression is an increased risk of the development of breast cancer. Depression may affect the endocrine and immune function (Kowal et al., 1955; Miller et al., 1993), which may have influence on cancer initiation and progression, including breast cancer. Importantly, women themselves widely believed that depression was a risk factor in the development of their breast cancer (Mitchell et al., 1995). However epidemiology evidences on the association between depression and breast cancer incidence are mixed and inconclusive.A great many of studies have assessed the association between depression and subsequent risks of breast cancer. A previous meta-analysis (Oerlemans et al., 2007) focusing on breast cancer pooled results from 7 prospective studies published before 2003 as a secondary analysis and reported a pooled relative risk estimated of 1.59 (95% confidence intervals, 0.74-3.44). Since then some cohort studies have been published, which provide stronger evidence of the association between depression and breast cancer. Therefore, we conducted a meta-analysis of cohort studies to describe the association between depression and risk of breast cancer.Materials and MethodsSearch strategyWe conducted a systematic literature search (up toApril 2014) of Medline, Embase, Web of Science for studies describing the association between depression and breast cancer. We used the following terms “depression”or “depressive disorder” or “major depressive disorder”or “depressive symptoms” and “breast cancer” or “breast carcinoma” combined with “cohort study” or “prospective study” or “follow-up study” or “longitudinal study”.In addition, studies from reference lists of all relevant publications and reviews were searched to identify potential pertinent studies.Study selectionStudies meeting the following criteria would be included in this meta-analysis: i) the study was a cohort design (prospective cohort or historical cohort); ii) the exposure was depression symptoms or depressive disorder which were measured by self-reported scales or structured clinical interview or clinician diagnosis; iii) the endpoint was diagnosis or report of breast cancer, all participants were free of any subtypes of cancer at the beginning of the study; iv) the study reported the RR or hazard risk(HR) with corresponding 95% CIs for the association between depression and breast cancer; and v) study was publishedin English. If multiple independent published reports were from a same cohort, only the latest one was included. Study selection was independently performed by two authors (S.H.L and D.X.X) and conflicts were resolved through discussion with the third reviewer (L.Z.X).Data extractionWe extracted the following information fromeach retrieved article: name of the first author, yearof publication, study location, characteristics of study population at baseline, duration of follow-ups, sample size, numbers of cases, depression and breast cancer measurements, adjusted effect estimate and corresponding 95% CIs, and variables used in multivariable analysis. Quality assessment was performed according to the Newcastle-Ottawa quality assessment scale for cohort studies (Wells et al., 2006) by two investigators (S.H.L and D.X.X). This scale allocates a maximum of nine points for quality of selection (0-4 points), comparability (0-2 points), exposure and outcome of study participants (0-3 points). The two authors discussed the implementationof this assessment tool and agreed on a method of implementation before their independent assessments ofstudies. The level of agreement between the two reviewers was calculated by another investigator (L.Z.X).Statistical analysisThe RRs were used as the common measure of association across studies, and the hazard ratios (HRs) were considered equivalent to RRs. Forest plot was produced to visually assess the RRs and corresponding 95% CIs across studies. Statistical heterogeneity across studies was estimated by I2 statistic. I2 values of 25%, 50%, 75% are regarded as cut-off points for low, moderate and 2003). The RRs were pooled using the fixed-effect modelif no or low heterogeneity was detected, or random-effect model otherwise (DerSimonian et al., 1986). In sensitivity analyses, we conducted leave-one-out analysis (Wallaceet al., 2009) for each study to examine the magnitude of influence of each study on pooled risk estimates. Subgroup analyses for study location, number of participants and cases, follow-up time, exposure measurement, smokingor alcohol drinking and study quality were conductedto examine the robustness of the primary results. Visual inspection of a funnel plot and Begg rank correlation test, Egger linear regression test (Begg et al., 1994;Egger et al., 1997) were used to evaluate the potential publication bias. The Duval and Tweedie nonparametric trim-and-fill procedure(Duval et al., 2000) was used to further assess the possible effect of publication bias. All statistical analyses were performed with STATA version 11.0 (StataCorp, College Station, Texas, USA). All tests were two sided with a significance level of 0.05.ResultsEligible studiesTotally 1705 articles were identified from the Medline, Embase, Web of Science. After the first round of screening based on titles and abstracts with aforementioned criteria, 1682 articles were excluded. Examining the articles remained in more details, nine articles (Hahn et al.,1988; Jacobs et al., 2000; Dalton et al., 2002; Nyklicek et al., 2003; Goldacre et al., 2007; Gross et al., 2010; Chen et al., 2011; Liang et al., 2011; Lemogne et al., 2013) met the inclusion criteria. The detailed reasons for exclusion were shown in Figure 1. Besides, one article (Schuurman et al., 2001) was found from the previous meta-analysis (Oerlemans et al., 2007) and one (Knekt et al., 1996) was identified by searching the reference lists. In total, elevenarticles were included in this meta-analysis.Study characteristicsCharacteristics of the eleven articles were showedin Table 1. These studies were published between 1988 and 2013. The sample size of studies varied from 1,533to 57,320, with a total of 182,241, and the number of breast cancer cases ranged from 20 to 728, with a totalof 2,353. With regard to study location, three studies were conducted in the USA, two studies in Taiwan, twoin Netherlands, one in France, one in the UK, one in Denmark, and one in Finland. In four of eleven studies, depression was measured by self-reported scales which were the Center for Epidemiologic Studies Depression Scale (CES-D), General Health Questionnaire (GHQ), Minnesota Multiphasic Personality Inventory(MMPI), and Ediburgh Depression Scale (EDS). Two studies used the Diagnostic Interview Schedule (DIS) and one used International Classification of Health Problems in Primary Care (ICHPPC) to define depression. The other four studies defined depression according to the International Classification of Disease, Ninth Revision, Clinical Modification or International Classification of Disease,Eighth Revision, Clinical Modification (ICD-9-CM or ICD-8-CM). The outcome of studies was ascertained by medical records or death certificates in seven studies, by self-report in two studies, and by combining self-report with medical records in the rest two studies. The eleven articles were assessed and were of moderate quality with a mean score of 6.9 (ranging from 6-8).All the included studies provided adjusted RRs. The major confounding factors adjusted included age, family history of breast cancer, cigarette smoking, alcohol intake, obesity, social status, and complications.Association between depression and risk of breast cancer The association between depression and breastcancer risk was shown in Figure 2. The majority of allthe eleven studies indicated a positive trend between depression and breast cancer (RR>1), but only two of them were statistically significant. At the same time one article (Nyklicek et al., 2003) reported that depression could reduce the risk of breast cancer in middle-aged women. With a moderate to high heterogeneity (I2=67.2%, p=0.001), the pooled analysis from random-effect model revealed that depression was not associated with breastcancer risk (RR,1.13; 95% CI 0.94 to 1.36).Subgroup analyses and sensitivity analysesTable 2 showed the results of subgroup analyses. We conducted subgroup analyses by study characteristics, such as study locations, number of study of participants and cases, duration of follow-up, exposure levels and study quality, while the results were not statistically significant. In addition, we conducted subgroup analyses according to the results whether or not adjusted by alcohol consumption or smoking, and neither alcohol consumption nor smoking altered the association.one showed that Jacobs et al’s study (Jacobs et al., 2000) and Goldacre et al’s study (Go ldacre et al., 2007) imposed the largest influence on the results. The pooled RRs were 1.24 (95%CI: 0.95-1.61) and 1.06 (95%CI 0.92-1.22) after excluding the two studies, respectively.Publication biasVisual inspection of funnel plot revealed some asymmetry (see supplementary Figure 1A). However,the Begg rank correlation test, Egger linear regressiontest provide no evidence of substantial publication bias (Begg’s test Z=1.25, p=0.213; Egger’s test t=-0.39,p=0.709). A sensitivity analysis using the trim-and-fill method was performed with 3 imputed studies, which produced a symmetrical funnel plot (see supplementary Figure 1B). The pooled RR incorporating the three hypothetical studies was smaller than the original results, but it still did not reach the statistically significant (RR, 1.04; 95% CI, 0.84-1.27).DiscussionThe study results were derived from eleven cohort studies which reported association between depression and risk of breast cancer. In all, our meta-analysis involved 2,353 cases of breast cancer and 182,241 participants.No significant association between depression and risk of breast cancer was found (RR, 1.13; 95%CI, 0.94 to 1.36) after adjustment for potential confounders. Furthermore, the association between depression and breast cancer persisted across subgroup analyses.Taking into account the impact of ethnic and geographic on the incidence of breast cancer, subgroup analyses by locations (European countries vs. USA vs. Taiwan) were conducted but no significant difference was found. As we know, different levels of exposure mayhave different effects on the study outcome. Therefore,we conducted subgroup analysis by exposure levels (depression symptoms vs. depressive disorder) which showed no statistically significant association between depression and breast cancer risk. Given that a long period was required to develop a detective tumor, subgroup analysis by the duration of follow-up were conductedand the results were not statistically significant as well, though the RR was elevated in the cohorts of more than10 years of follow-up. There were studies identifiedthat depression individuals may engage more unhealthy behaviors that predispose them to further onset of cancer, such as smoking, alcohol consumption, lack of physical activity (Son et al., 1997; Strine et al., 2008). But the subgroup analyses according to the results that whetheror not adjusted by smoking and alcohol consumption didnot find significant association.A meta-analysis conducted by Marjolein EJ Oerlemanset al. (2007) in 2007 investigated the relationship between depression and overall cancer risk. The previous metaanalysis also identified association between depressionand breast cancer as a secondary analysis. The secondaryanalysis included seven prospective studies which involved 111756 participants and 1601 cases and reported no significant association (RR, 1.59; 95%CI, 0.74-3.44). Our meta-analysis, with four more cohort (Goldacre et al., 2007; Chen et al., 2011; Liang et al., 2011; Lemogne et al., 2013) studies and one update study (Gross et al., 2010), demonstrates no evidence of association between depression and breast cancer, which is consistent with the previous meta-analysis. However, we noticed that the previous review found depression might be a risk factor for breast cancer (RR, 2.5; 95%CI, 1.06-5.91) if study population were followed more than 10 years. In our review, this association in subgroup analysis by follow-up more than 10 years was not proved. To our knowledge, the larger size of participants, the stronger evidence of the study. The combined results of our meta-analyses are more credible with relatively narrow confidence intervals. Considering the limited number of the included studiesof the previous meta-analysis, we can not conclude that there is significant association between depression and breast cancer.Experimental animal studies, human studies andclinical evidence suggest that depression may put an influence on the development of breast cancer through several mechanisms, such as impairing immune function, causing an aberrant activity of the hypothalamic-pituitary- adrenal axis and inhibiting DNA repairmechanisms (Kiecolt-Glaser et al., 2002; Reiche et al., 2005; Soygur et al., 2007). However, epidemiological research evidences did not indicate the presence of sucha relationship between depression and breast cancer. The and epidemiological studies may be explained by two reasons. On the one hand, the strength of experimental evidence may be compromised due to species differences, inconsistent of laboratory conditions and the measurement of biomarker. Some experiments could not be replicated by different investigators. On the other hand, epidemiological studies may have some methodological flaws, such as insufficient follow-up duration, different definitions and measurement of exposure, the size of sample and so on. Overall, evidence supporting that depression increases the risk of breast cancer are insufficient.There are two strengths in our meta-analysis. Firstly,all studies in the present analyses were cohort studies,which minimized the selection and recall bias. Although our review is an updated meta-analysis, it provides robust and credible conclusion for the association between depression and breast cancer. Secondly, most of studies included in this meta-analysis had average follow-up times more than 10 years. Sufficiently long follow-up duration is necessary because most cancers have a latent period of a few years or even decades (Spratt et al., 1996; Friberget al., 1997). Thus, our results based on long follow-up duration studies could indicate that the depression might not increase the risk of breast cancer.Limitations: A few limitations of our meta-analysis should be acknowledged. Firstly, depression was only measured on the basis of a single baseline measure, which was clearly not identical to depression diagnosis. During the follow-up duration, the exposure intensity of subjects would change. Penninx et al (1998) (Penninx et al., 1998) proved that repeated assessment of depressive symptoms yielded positive association with later developmentof some cancers, in contrast to single measurements. Therefore, a one-time assessment of depression withno measure of duration weakens the test of hypothesis.Secondly, no less than 8 different scales were used for the measurement of depression in the 11 original studies. It may add to the multiple conceptual problems concerned with the definition of depression (Buntinx et al., 2004), which could increase the heterogeneity in our metaanalyses. In conclusion, available epidemiological evidencesare insufficient to support association between depression and the development of breast cancer. Given the high prevalence and morbidity of depression and breast cancer, the results of this meta-analysis not only can act as the clue of the etiology, but can provide the evidence to women who believed that depression could increase the risk of breast cancer.Acknowledgements。

贝叶斯确证理论及其局限性Chapter 1: Introduction- Background information about Bayes' Theorem- Purpose of the paper- Overview of the main points discussed in the paperChapter 2: Understanding Bayes' Theorem- Explanation of Bayes' Theorem- Use of Bayes' Theorem in decision-making and scientific research- Comparison to frequentist approachChapter 3: Limitations of Bayes' Theorem- Assumptions made in Bayes' Theorem- Probability estimates and subjectivity- Small sample sizes- Dependence on prior knowledgeChapter 4: Applications and Criticisms- Examples of how Bayes' Theorem has been applied in various fields- Criticisms of Bayes' Theorem by scholars- Counterarguments to criticismsChapter 5: Conclusion and Future Directions- Summary of key points in the paper- Implications of limitations of Bayes' Theorem- Potential areas for future research on Bayes' Theorem and related topicsChapter 1: IntroductionBayes' Theorem is a statistical concept widely applied in decision-making, artificial intelligence, machine learning, and scientific research. Bayes' Theorem provides a framework for updating probabilities based on new evidence and prior knowledge. It was named after the eighteenth-century English statistician, Reverend Thomas Bayes, who developed the theory to solve the problem of inverse probability. Since its inception, Bayes' Theorem has been applied in numerous fields to make predictions, inferences, and to uncover causality.The purpose of this paper is to provide an overview of Bayes' Theorem, its applications, and its limitations. The paper will explore the assumptions behind Bayes' Theorem, the subjective nature of probability estimates, and the dependence on prior knowledge. Furthermore, the paper will examine the criticisms leveled at Bayes' Theorem and how these criticisms have been countered. Finally, the paper will dispel some common misconceptions about Bayes' Theorem and suggest areas for future research.Chapter 2: Understanding Bayes' TheoremBayes' Theorem is a mathematical formula that is used to update the probability of an event occurring based on new evidence. It is often used in decision-making, scientific research, and artificial intelligence systems. The fundamental concept behind Bayes' Theorem is conditional probability. Conditional probability describes the probability of an event occurring given that some other event has occurred. For instance, the probability of heavy rain is higher given that there has been an increase in cloud cover.Bayes' Theorem is expressed mathematically as:P(A|B) = P(B|A) P(A) / P(B)Where:P(A) is the prior probability of event A.P(B) is the probability of observing evidence B.P(B|A) is the probability of observing evidence B given that event A has occurred.P(A|B) is the posterior probability of event A after observing evidence B.The numerator of the equation represents the likelihood of the event happening if the evidence is true, while the denominator represents all possible outcomes of the evidence being true. Bayes' Theorem allows us to update our beliefs about the probability of an event after observing new evidence, given what we already know. The advantages of using Bayes' Theorem include:- It allows the incorporation of new data that may render previous conclusions obsolete, thus providing a more accurate estimation. - It is useful in making predictions and inferences about the future. - It can handle complex situations of multiple causes, as long as prior probabilities can be established.Chapter 3: Limitations of Bayes' TheoremDespite its numerous applications, Bayes' Theorem suffers fromlimitations that are important to understand. The following are key limitations of Bayes' Theorem:Assumptions made in Bayes' TheoremThe practical use of Bayes' theorem depends on several assumptions made regarding the nature of the problem being analyzed. These assumptions include:- Independence: It is assumed that the occurrence of one event does not affect the occurrence of another event. Yet, in real-world scenarios, variables are often interrelated.- Stationarity: It is assumed that the probabilities remain constant over time. However, in some instances, the probabilities may change over time.- Normality: The results of a study that uses Bayes' theorem may only be valid if the population distribution is normal. This is not always the case.Subjectivity in Probability EstimatesBayes' theorem requires the estimation of prior and posterior probabilities. In some instances, the prior probability may be subjective. This is particularly true when knowledge and data are limited or unavailable. In such instances, the subjective nature of the prior probability may cause bias in the final estimation. Small Sample SizesBayes' theorem may result in unreliable outcomes if the sample size is too small. In such cases, the estimation is subjected to the uncontrollable statistical fluctuations, which often result in an over-reliance on subjective reasoning.Dependence on Prior KnowledgeBayes' theorem is heavily reliant on prior knowledge for the estimation of probabilities. If prior knowledge is biased or insufficient, the resulting estimation may be inaccurate. Updating prior probabilities is also subjective, and it may lead to inconsistent outcomes.In conclusion, Bayes' Theorem is a powerful tool that has been widely used in various fields. Its application is dependent on certain assumptions that may not always be valid. Additionally, the estimation of probability is often subjective, leading to possible inaccuracies in outcomes. Despite its limitations, Bayes' Theorem remains a fundamental concept in statistics and decision-making. The next chapter will delve into the applications of Bayes' Theorem in various fields.Chapter 4: Applications of Bayes' TheoremBayes' Theorem has been applied in various fields, particularly in decision-making, scientific research, and artificial intelligence. The following are some of the key applications of Bayes' Theorem: Medical DiagnosisBayes' theorem is employed in medical diagnosis to calculate the probability of a patient having a particular condition based on their symptoms and medical history. The theorem is used to update physicians' prior knowledge of the patient's condition with new diagnostic test results. For instance, if a patient is hospitalized for chest pains, their chances of having a heart attack can be estimated using Bayes' Theorem after considering other significant risk factors like age, smoking status, and cholesterol levels.Machine LearningBayes' theorem is an essential element in creating machine learning models. Through its application, developers can create statistical models that help systems predict behaviors, classify data, and recognize patterns. Bayes' coefficient is essential in this field since algorithms rely on it to make predictions based on previous data.Stock Market PredictionBayes' theorem provides traders with a framework for making investment decisions. By predicting future market conditions using past performance and analyzing current trends, traders can calculate the probability of future market prices using Bayes' Theorem to make more informed decisions.Natural PhenomenaThe theorem has been used in the prediction of natural phenomena such as earthquakes, floods, and storms by predicting the probability based on historical data. Through the analysis of data, scientists can identify patterns and make informed predictions.Chapter 5: Criticisms and Controversies of Bayes' TheoremBayes' Theorem has generated numerous criticisms and controversies, despite its widespread use. These criticisms are primarily focused on its relevance in real-world scenarios and how it's applied in practice.Misapplication of Bayes' TheoremOne of the most significant criticisms of Bayes' Theorem is its incorrect application in real-world situations. The theorem depends on certain assumptions that are not always valid or difficult to estimate correctly, leading to misuse. This problem is most prevalent in the fields of law enforcement, social science, and medicine, where the use of Bayes' Theorem can lead to wrongful conviction, inappropriate treatment, and misjudgment of evidence. Subjectivity in Probability EstimatesAnother significant criticism is the fact that the estimation of probabilities is subjective and relies heavily on prior beliefs. In some cases, these priors may be biased or based on limited knowledge, leading to inaccurate results.Dependence on Prior Knowledge and Sample SizeCritics of Bayes' Theorem also argue that the theorem is heavily reliant on prior knowledge. If prior knowledge is biased or insufficient, this diminishes the credibility of the resulting estimate. Additionally, the theorem requires significant sample sizes to generate accurate results. When sample sizes are too small, the outcomes are less reliable.Controversies Surrounding Bayesian StatisticsApart from criticisms of the theorem itself, there are some controversies surrounding Bayesian statistics caused by philosophical differences between the Bayesian and non-Bayesian camps. The Bayesian camp argues that probability is subjective and that prior probabilities must depend on the available evidence. The non-Bayesian camp, on the other hand, believes in objective probability and prefers to use only observable data and tests.ConclusionBayes' Theorem is a powerful tool with a range of applications in various fields. Despite being a widely accepted system, it has received significant criticism, particularly regarding its relevance and accuracy in real-world scenarios. Nonetheless, Bayes' Theorem remains a fundamental concept in statistics and decision-making, and its use will continue to grow in the years ahead. Future research should focus on developing methods for improving how Bayes' Theorem is applied and the quality of prior knowledge used in estimation.。

The US consumer price indexmay be overstating the infla-tion rate, thereby distortingcalculations of inflation adjustments in both govern-ment expenditures and income tax brackets and swelling the federal deficit.HANGES IN the consumer price index (CPI) provide the most commonly used measure of infla-tion in all countries (see box). In arecent study, the US Advisory Commis-sion to Study the Consumer Price Index (more commonly known as the Boskin Commission, whose chairman was Michael Boskin, former chief of the US Council of Economic Advisers) estimated that the USCPI overstated inflation by 1.1 percentagepoint in 1996 and by slightly more in eachof the previous 20 years. Thus, althoughthe official rate of inflation for 1996 was 2.9percent, the true rate may have been in the neighborhood of 1.8 percent. This upward bias arises because the CPI methodology does not adequately capture shifts in con-sumer purchases when relative prices move, the effects of changes in the qualityof goods and services, the introduction ofnew products, or the growing number of discount stores. While some experts have disputed that the upward bias is as large as has been suggested by the Commission,there is a growing consensus that there may indeed be significant bias.Upward bias in the official inflation rate has important implications. First, real wages—which were widely thought, on the basis of official data, to have stagnated over the last two decades—may, in fact, have increased considerably. Second, in regard to fiscal policy, upward bias has considerable budgetary costs: expenditures indexed to the CPI rise by more than is needed to offset inflation, and inflation adjustments made to tax brackets are overstated, resulting in reduced tax revenues. Recent estimates indicate that if the current inflation bias continues for the next 10 years, the federalgovernment deficit will increase on this account alone by $140 billion, and $650 bil-lion will be added to the national debt by the end of the period (see chart).The Boskin Commission’s report identi-fied and quantified three sources of bias, allof which arise because of limitations in the methodology used to calculate the CPI (seetable):•Quality change and new product bias ,the largest source of bias, arises because the CPI does not immediately take intoaccount either improvements in the quality of goods and services or the introduction of CHow the US CPI is computed In the United States, the consumer price index (CPI) is used to estimate the overall price level in the consumer sector of the economy each month. The US Department of Labor’s Bureau of Labor Statistics (BLS) is responsible for calculating the CPI, which is based on individual pricesfor a fixed market basket of goods and services, which includes food, clothing, shelter, fuel,transportation, medical services, and other ing statistical sampling techniques to select specific items, the BLS collects prices each month for about 71,000 goods and services from about 22,000 outlets in 44 geographic areas.For example, the cost of housing is included in the data collection by surveying about 5,000renters and 1,000 homeowners each month. The price quotations the BLS obtains are then com-bined to form the consumer price index. Some simplifying assumptions have to be made to make this complex calculation practicable. The formula the BLS uses to aggregate all of these prices assumes that consumers purchase fixed quantities of goods—that is, that their spending patterns remain the same—over time. The CPI, then, is designed to reveal how much it costsconsumers to purchase the same market basket of goods and services today compared withwhat it cost in a previous month or year.20Finance & Development / June 1997Bias in the US Consumer Price Index:Why It Could Be ImportantPAU L A. A R M K N E C H T A N D PAU L A R. D E M A S IPaul A. Armknecht,a US national, was formerly Assistant Commissioner for Consumer Prices with the US Department of Labor’s Bureau of Labor Statistics and is cur-rently a Consultant to the Real Sector Division of the IMF’s Statistics Department.Paula R. De Masi,a US national, is an Economist in the World Economic Studies Division of the IMF’s Research Department.WORLD ECONOMY IN TRANSITIONnew products. To the extent that the CPI fails to account for changes in quality, the index will not reflect “true” changes in prices. And new products need to be incor-porated into the CPI on a timely basis, so that the early declines in price that are a normal part of the product life cycle are captured.•Substitution bias occurs because the formula used for CPI calculations assumes that consumers purchase a constant mix of various goods and services despite changesin their relative prices. In actuality, if the price of one good rises relative to that of another good, consumers will tend to sub-stitute cheaper goods for higher-priced ones. Because the weights of goods in the CPI are adjusted infrequently (about once every 10 years), substitution is not taken into account.•Outlet substitution bias occurs because the CPI does not adequately take into account the extent to which new discount stores have offered lower prices and enticed consumers away from the traditional out-lets that tend to be more fully represented in the CPI market basket.To eliminate the various biases, the Commission recommends replacing the method used in calculating the CPI with one that more accurately takes into account changing spending patterns. Other changes recommended include adopting new procedures for annual updates of weights and revisions to historical data,changing the price data and methods of collection, and establishing a committee of outside experts to review and advise the US Department of Labor’s Bureau of Labor Statistics on statistical issues.The Commission’s conclusions have been criticized by some commentators. Most ofthe criticism has been directed at the large estimates of quality and new product bias.Measuring quality improvements is partic-ularly difficult because direct quantitative evidence is scarce, and no new substantive information on this issue was provided inthe Commission’s report. Some critics have noted that the report does not take into account the fact that the quality of some goods and services included in the CPI mar-ket basket has deteriorated.Although the debate about upward bias in the CPI has been most active in the United States, the findings of the Com-mission’s study are relevant more generally,since many countries use methodologies that have much in common with that used in the United States. Analyses of the Canadian CPI suggest that there may be anupward bias of 0.5–1 percent, somewhatlower than in the United States, reflecting in part the more frequent updating inCanada of the weights of the goods and ser-vices in the CPI market basket. A study of the United Kingdom’s retail price index suggests a plausible range of bias of 0.35–0.8 percent, although further work is under way to assess whether the bias may actually be larger.More generally, the magnitude of bias in other countries depends on, among other factors, the frequency with which the CPI weights and the items sampled are updated; the extent to which new and improved products are brought to market;the formula used in estimation; and theextent to which quality adjustments are made. For example, indexes of consumerprices in countries where the weights used are updated annually—such as Norway,Sweden, and the United Kingdom—are likely to be less susceptible to substitution bias. Although most industrial countries—including the United States—make some attempt to allow for quality changes, theyare not entirely successful in eliminatingthis form of bias. In most of the developing and transition countries, however, no qual-ity adjustments are made, suggesting thatthis form of bias may have an important impact on their consumer price indexes—and, thus, on the inflation rates they indicate—particularly when newly opened markets increase the variety and quality of goods and services available to con-sumers.21Finance & Development / June 1997For a more detailed discussion of the data collec-tion procedures and methodology used to pre-pare the US consumer price index, see Paul A.Armknecht, 1996, “Improving the Efficiency of the U.S. CPI,” IMF Working Paper No. 96/103(Washington: International Monetary Fund). This article is derived from a box entitled “United States: Sources and Implications of Bias in the Consumer Price Index” published in the Spring 1997 edition of the IMF’s WorldEconomic Outlook (Washington).Reference:United States, Advisory Commission toStudy the Consumer Price Index, 1996, Toward a More Accurate Measure of the Cost of Living (Washington).Impact of correcting a 1 percentage point overstatementin the CPI on the US deficitO u t l a y r e d u c t i o n o r r e v e n u e i n c r e a s eReduction in deficit due to change in:RevenuesDebt service Social security outlays Other outlays Source: United States, Congressional Budget Office, 1997, The Economic and Budget Outlook (Washington).-1501998199920002001200220032004200520062007-120-90-60-30O v e r a l l d e f i c i t r e d u c t i o n i n 2007Sources of bias Percent per year Quality change/new product bias 0.6Substitution bias 0.4Outlet substitution bias 0.1Total 1.1(Plausible range) (0.8–1.6)Source: United States, Advisory Commission to Study the Consumer Price Index, 1996, Toward a MoreAccurate Measure of the Cost of Living , Final Report to the Senate Finance Committee (Washington).Sources of bias in US consumer price index, 1996F &D。

Sample Selection Bias as a Specification ErrorJames J.HeckmanEconometrica,Vol.47,No.1.(Jan.,1979),pp.153-161.Stable URL:/sici?sici=0012-9682%28197901%2947%3A1%3C153%3ASSBAAS%3E2.0.CO%3B2-J Econometrica is currently published by The Econometric Society.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use,available at/about/terms.html.JSTOR's Terms and Conditions of Use provides,in part,that unless you have obtained prior permission,you may not download an entire issue of a journal or multiple copies of articles,and you may use content in the JSTOR archive only for your personal,non-commercial use.Please contact the publisher regarding any further use of this work.Publisher contact information may be obtained at/journals/econosoc.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals.For more information regarding JSTOR,please contact support@.Wed Apr1811:20:522007You have printed the following article:Sample Selection Bias as a Specification ErrorJames J.HeckmanEconometrica ,Vol.47,No.1.(Jan.,1979),pp.153-161.Stable URL:/sici?sici=0012-9682%28197901%2947%3A1%3C153%3ASSBAAS%3E2.0.CO%3B2-JThis article references the following linked citations.If you are trying to access articles from anoff-campus location,you may be required to first logon via your library web site to access JSTOR.Please visit your library's website or contact a librarian to learn about options for remote access to JSTOR.[Footnotes]2Wage Comparisons--A Selectivity BiasReuben GronauThe Journal of Political Economy ,Vol.82,No.6.(Nov.-Dec.,1974),pp.1119-1143.Stable URL:/sici?sici=0022-3808%28197411%2F12%2982%3A6%3C1119%3AWCSB%3E2.0.CO%3B2-L2Comments on Selectivity Biases in Wage ComparisonsH.Gregg LewisThe Journal of Political Economy ,Vol.82,No.6.(Nov.-Dec.,1974),pp.1145-1155.Stable URL:/sici?sici=0022-3808%28197411%2F12%2982%3A6%3C1145%3ACOSBIW%3E2.0.CO%3B2-YReferences1Regression Analysis when the Dependent Variable Is Truncated NormalTakeshi AmemiyaEconometrica ,Vol.41,No.6.(Nov.,1973),pp.997-1016.Stable URL:/sici?sici=0012-9682%28197311%2941%3A6%3C997%3ARAWTDV%3E2.0.CO%3B2-FLINKED CITATIONS -Page 1of 2-2Specification Bias in Estimates of Production FunctionsZvi GrilichesJournal of Farm Economics ,Vol.39,No.1.(Feb.,1957),pp.8-20.Stable URL:/sici?sici=1071-1031%28195702%2939%3A1%3C8%3ASBIEOP%3E2.0.CO%3B2-V 4Wage Comparisons--A Selectivity BiasReuben GronauThe Journal of Political Economy ,Vol.82,No.6.(Nov.-Dec.,1974),pp.1119-1143.Stable URL:/sici?sici=0022-3808%28197411%2F12%2982%3A6%3C1119%3AWCSB%3E2.0.CO%3B2-L8Dummy Endogenous Variables in a Simultaneous Equation SystemJames J.HeckmanEconometrica ,Vol.46,No.4.(Jul.,1978),pp.931-959.Stable URL:/sici?sici=0012-9682%28197807%2946%3A4%3C931%3ADEVIAS%3E2.0.CO%3B2-F9Asymptotic Properties of Non-Linear Least Squares EstimatorsRobert I.JennrichThe Annals of Mathematical Statistics ,Vol.40,No.2.(Apr.,1969),pp.633-643.Stable URL:/sici?sici=0003-4851%28196904%2940%3A2%3C633%3AAPONLS%3E2.0.CO%3B2-311Comments on Selectivity Biases in Wage ComparisonsH.Gregg LewisThe Journal of Political Economy ,Vol.82,No.6.(Nov.-Dec.,1974),pp.1145-1155.Stable URL:/sici?sici=0022-3808%28197411%2F12%2982%3A6%3C1145%3ACOSBIW%3E2.0.CO%3B2-Y 12Specification Errors and the Estimation of Economic RelationshipsH.TheilRevue de l'Institut International de Statistique /Review of the International Statistical Institute ,Vol.25,No.1/3.(1957),pp.41-51.Stable URL:/sici?sici=0373-1138%281957%2925%3A1%2F3%3C41%3ASEATEO%3E2.0.CO%3B2-BLINKED CITATIONS -Page 2of 2-。

Data source: Zhang Lianwen, Guo Haipeng. "Introduction to Bayesian networks". Science Press, 2006 Thomas Leonard, John.J.Hsu. "Bayesian method" (English version)Industry Press, 2004A Bayesian ruleBias's Law (Bayes'theorem/Bayes theorem/Bayesian law) Bias was a basic tool called "Bias's law", although it is a mathematical formula, but the principle can be understood without digital. If you see a person always do some good, then that person will probably be a good man. That is to say, when cannot accurately knows the essence of a thing, can how much depends on the specific nature of the events and things appear to judge the nature of probability. It is expressed in mathematical language: support a property of the event of the possibility, the attribute set is big.The basic conceptBias's law is also known as the Bias theorem, Bias's law is the application of probability and statistics of the observed phenomena on subjective judgments about the probability distribution (i.e., prior probability) standard correction method. The so-called Bayesian rule, when analyzing samples to close to the overall number, probability sample of events will be close to the overall probability of events. But the behavioral economists found, people in the decision-making process is often not followed by Bayesian rule, but given recent events and the latest experience with more weight, recent events have too much weight to make judgments in the decision-making and. In the face of the complex and the general questions, people often take shortcuts, on the basis of probability rather thanaccording to probability decision. System of this classic model called "deviation deviation". Because of the psychological bias, investors are not in decision making when absolutely rational, behavior deviation, and the impact of price changes on the capital market. But for a long time, because of the lack of a strong alternative tools, economists have to adhere to the Bayes rule in the analysis.PrincipleUsually, the event A in the event B (happen) probability, probability and event B in the event A conditions are not the same; however, these two are determined, the Bayes rule is this statement. As a normative theory, Bayes rule is effective for all probabilistic interpretation; however, frequency, and Bayesian principle regarding the probability to be assigned a different view in the application: frequency, according to the random events, or the number of total sample assignment probability; Bayesian theory depending on the unknown proposition to assign probability. As a result, Bayesians have had more chances to use Bayes rule. Bias's law of random events A and B conditional and marginal probabilities. \Pr (A|B) = \frac{\Pr (A, B |), \Pr (A)}{\Pr (B)}\propto L (A | \ B), \Pr (A), where L (A|B)! Is the possibility of A occurred in the B case. In the Bayesian rule, each noun has a name: Pr (A) is the prior probability or probability of edge A. It is called "a priori" because it does not consider any aspect of B. Pr (A|B) is known B occurred after A conditional probability, also due to the self value of B and A calledthe posterior probability. Pr (B|A) is known A occurred after B conditional probability, also due to the self value of A and B called the posterior probability. Pr (B) is the prior probability or probability of edge of B, are also normalized constant (normalized constant). According to these terms, the Bayes rule can be expressed as: the posterior probability = (similarity * prior probability) / normalized constant that is to say, the product of a posteriori probability and is proportional to the prior probability and similarity. In addition, the ratio of Pr (B|A) /Pr (B) is also sometimes referred to as the standard similarity (standardised likelihood), the Bayes rule can be expressed as: the posterior probability = standard similarity * prior probability.The example analysisCase 1: the monopoly market, only an enterprise A provides products and services. Now consider whether to enter the enterprise B. Of course, A enterprise will not sit back and watch B and completely indifferent to. B know, whether can enter, depends entirely on the A enterprise to prevent the entry and the cost of size. Challenger B do not know the original monopolist A belongs to the high block cost type or low block cost type, but B know, if A belongs to the high block cost type, the probability of B in the market of A block is 20% (high profits, at A in order to maintain the monopoly regardless of the cost to piece together the life; if the block) A belongs to the low blocking probability B to enter the market cost type,when the A block is 100%. The game began, according to B probability A belongs to the high block cost of enterprises is 70%, therefore, the B estimate oneself in the market, by the probability A block: 0.7 * 0.2+0.3 * 1=0.44 0.44 is the prior probability type given in B A, A may use blocking behavior probability. When B entered the market, A does block. Using the Bayes rule, according to block the observable behavior, according to B probability A belongs to the high block cost of enterprises into A belongs to the probability of =0.7 high costs of enterprises (A belongs to the high cost of the prior probability of enterprise) x 0.2 (probability of high cost of enterprises in the new market enterprises by) ÷ 0.44=0.32 according to this new probability, B estimates themselves in the market, by the probability A block: 0.32 × 0.2+0.68 × 1=0.744 if B again to enter the market, A was blocked. Using the Bayes rule, according to block the observed behavior, B thinks the probability A belongs to the high block cost of enterprises into A belongs to the probability of =0.32 high costs of enterprises (A belongs to the high cost of the prior probability of enterprise) x 0.2 (probability of high cost of enterprises in the new market enterprises by) ÷ 0.744=0.086 thus, according to the blocking behavior of A once again, B on A type judgment has changed gradually, more and more inclined to judge for the low cost A to enterprise. The above example shows that, in a dynamic game of incomplete information, has the function of transmitting information in one act. Although the A enterprise may be the high cost of enterprise, butenterprise A continuous market entry deterrence, to B enterprises to A enterprise is low block impression cost of enterprises, thus enterprise B stopped coming into the market action. It should be pointed out is, information behavior is a cost. If there is no cost to this behavior, who can follow, then, this kind of behavior is not up to the purpose of transmitting information. Only in the act requires considerable cost, so that others can not easily imitated, this behavior can play the role of information transmission. Transfer payment information cost is caused by incomplete information. But we can not say that the incomplete information is necessarily a bad thing. Research shows that, in the repeated prisoner's dilemma game times are limited, incomplete information can lead to bilateral cooperation. The reason is: when the information is incomplete, participants in order to obtain the long-term interests of cooperation brings, not premature exposure of his nature. That is to say, in a long-term relationship, a person to do good or bad, often does not depend on his nature is good is bad, but to a large extent depends on the extent to which other people think he is a good man. If the other person doesn't know his true colors, a bad man will do good to cover themselves in a quite long period.Case two: consider a medical diagnosis problem, there are two possible hypotheses: (1) patients with cancer. (2) patients without cancer. The sample data from a laboratory test, it also has two possible results: positiveand negative. Suppose we have a priori knowledge: only 0.008 of the people in all the population prevalence. In addition, laboratory testing of disease in 98% of patients may return to positive results, no patients had 97% may return a negative result. The above data can be represented by the following formula: the probability P (cancer) =0.008, P (non cancer)=0.992 P (+ |cancer) =0.98, P (|cancer negative (positive) =0.02 P | without cancer) =0.03, P (negative | without cancer) =0.97 if you have a new patient, the test returns positive if the patient will determine, for cancer? We can calculate the maximum a posteriori hypothesis: P (+ |cancer) P (cancer) =0.98*0.008 = 0.0078 P (positive | without cancer) *p (without cancer) =0.03*0.992 = 0.0298, therefore, should be judged as no cancer. DifferenceHarsanyi transformation and Bayesian rule in 1967, Harsanyi (JohnHarsanyi) points out the game with incomplete information of all the old definition can not change its essence is under the condition of the new model into a complete but imperfect information game, it only needs to add a different set of rules from nature in the choice of the initial action. In the old definition, game theory often point out game of incomplete information can not be analyzed, while the Harsanyi ideas make all this change. The old definition is described in this way: in complete information game, all players know the rules of the game, otherwise the game is a game of incomplete information. Although not that old Harsanyi definition is aproblem, but the fact that people view has changed, now believes that in the original definition, the game was converted to a game of incomplete information. In the game, including participation in the game may pay is not very clear, but some understanding of payment. In general, represented by the information of subjective probability distribution. Is the probability to construct various game payment based on grouping, can form a specific payment collection. For example, a and B are choice of strategy, it can be considered, a selection of a certain strategy, B to select several strategies, these strategies are grouped according to B of the probability of occurrence. Usually build a game tree can better express all this. The key point of Harsanyi doctrine assumed that all the participants have a common understanding, to adopt the strategy of the probability of occurrence is a common knowledge. The implied meaning is: participants at least a little discloses to our assumptions. The division of time in the information structure of a game, not trying to decide in what can be inferred from the other people involved in the campaign. The prior probability is present, as part of the game rules, a player must be held about other players types of prior beliefs, at the same time, their actions after observation, is to assume that they follow the equilibrium behavior, and then update their beliefs.Related principlesThe prior probability and posterior probability P (H) expressed in the absence of training data before assuming the initial probability h owned. P (H) is known a priori probability H. The prior probability reflects on the H is a correct hypothesis opportunity background knowledge without the prior knowledge, can simply be each candidate that gives the same prior probability. Similarly, P (D) represents the prior probability of the training data of D, P (D|h) represents the probability of D assumptions h established. In machine learning, we are concerned with P (h|D), which established the probability h of a given D, called the H posterior probability. The maximum a posteriori hypothesis learning device in candidate hypotheses for a given data set H D the most likely hypothesis h, h is known as the maximum a posteriori hypothesis (MAP) determined by the method of MAP is calculated for each candidate hypothesis using the Bayesian posterior probability, calculation formula is as follows: h_map=argmax P (h|D) (P (=argmax D|h) *P (H)) /P (D) =argmax P (D|h) *p (H) (H belongs to the set H) the last step, removed the P (D), because it is not dependent on H. The maximum likelihood hypothesis in some cases, can be assumed that the H of each hypothesis have the same prior probability, so that the formula can be simplified, consider only the P (D|h) to find the most likely hypothesis. H_ml = argmax P (D|h) H belongs to the set H P (D|h) is oftenreferred to as a h D data likelihood, and the P (D|h) maximum is called the maximum likelihood hypothesis.Characteristic(1) Bias classification does not take an object is assigned to a class, but through calculating probability belonging to a class, the class with maximum probability is the object belongs to the class of;(2) general Bias in the classification of all attributes are potentially play a role, which is not of one or several attribute determines the classification, but all attributes are involved in classification;Bias (3) attribute classification object can be discrete, continuous, and can also be mixed.Bias theorem gives the optimal minimum error solution, can be used for classification and prediction. In theory, it looks perfect, but in practice, it can not directly use, it needs to know the exact probability distribution of evidence, but in fact we cannot give evidence and probability distribution of the exact. We therefore in many classification methods will make some assumptions to approach Bias theory.文献来源：张连文,郭海鹏.《贝叶斯网引论》.科学出版社,2006.Thomas Leonard，John .J.Hsu.《贝叶斯方法》（英文版）.机械工业出版社,2004.关于贝叶斯法则贝叶斯法则（Bayes'theorem/Bayes theorem/Bayesian law）贝叶斯的统计学中有一个基本的工具叫“贝叶斯法则”，尽管它是一个数学公式，但其原理毋需数字也可明了。

u校园全新版大学英语2视听说答案一、单项选择（每小题1 分，共10分）1. Artists cannot remain _____ , though, when they become bored, their work begins to show a lack of continuity in its appeal and it becomes difficult to sustain the attention of the public. [单选题]A. idle(正确答案)B. lazyC. profoundD. intricate2. Many English people in the 1920s and 1930s thought Chaplin’s Tramp a bit, well, “crude”, while the working-class audiences were more likely to ______ for a character who revolted against authority. [单选题]A. objectB. admitC. favorD. clap(正确答案)3. Faced with sharing a dinner of raw pet food with the cat, many people in wheelchairs I know _______ the system for a few extra dollars. [单选题]A. drewB. bleed(正确答案)C. revoltedD. roused4. It’s a ________ to know that life eventually gave Charlie Chaplin the stability and happiness it had earlier denied him. [单选题]A. relief(正确答案)B. suspenseC. provisionD. recession5. Deep down, caseworkers know that they are being made fools of by many of their clients, and they feel they are entitled to have clients bow to them as ___________. [单选题]A. professionB. commitmentC. nonsenseD. compensation(正确答案)6. In business bribery, we may also include large payments made to the powerful__________ families or their close advisers in order to secure arms sales or major petroleum or construction contracts. [单选题]A. ruling(正确答案)B. appealingC. reigningD. promising7. The prime mover behind the project, Luca Cavalli-Sforza, a Stanford professor, labored with his colleagues for 16 years to create ______________the first genetic map of the world. [单选题]A. nothing more thanB. nothing less than(正确答案)C. anything butD. something but8. Someone is always at my_________ reminding me that I am the granddaughter of slaves. But it fails to register depression with me. [单选题]A. handB. elbow(正确答案)C. sideD. Stand9. In fact, there is no scientific _______ for theories advocating the genetic superiority of any one population over another. [单选题]A. basis(正确答案)B. cueC. biasD. bale10. What the eye sees as racial differences—between Europeans and Africans, for example—are mainly a way to ________ to climate as humans move from one continent to another. [单选题]A draftB.adoptC. C. abuseD. D. adapt(正确答案)二、选词填空（每小题1 分，共10分,填字母）Directions: Fill in each of the blanks with an appropriate word from the box. You may not use any of the words more than once.A. rawB. investmentC. concerningD. idleE. scratchF. certifyG. humbleH. distinctI. executeJ. discounted11. Hundreds of workers sat _________ on the factory floor waiting for the assembly line to start again. [填空题]空1答案：D12. The European Union is made up of 27 nations with ______ cultural, linguistic and economic roots. [填空题]空1答案：H13. Now that we have approval we may _________ the scheme as previously agreed. [填空题]空1答案：I14. I prefer to eat vegetables _________, not cooked, because I believe that is better for my health. [填空题]空1答案：A15. This is to ________ that the holder of this certificate has been awarded top prize in the English-speaking contest. [填空题]空1答案：F16. The local government has given priority to the construction of infrastructure to attract more foreign ___________. [填空题]空1答案：b17. We had only two weeks to tour Malaysia, which was hardly enough to _______ the surface. [填空题]空1答案：E18. Employees at _________ jobs have to carefully weigh up the employer’s words and closely watched their expression. [填空题]空1答案：G19. The speech which he made _________ the project has been very encouraging. [填空题]空1答案：C20. Some medical experts believe the chances of an explosive spread of the disease to Europe cannot be ___________. [填空题]空1答案：J三、阅读理解（每小题2 分，共20分）Directions: In this section there are three passages. Each passage is followed by some questions or unfinished statements with four choices marked [A], [B], [C], and [D]. You are supposed to read the passage and make the best choice to complete each question or unfinished statement.Question 21 to 25 are based on the following passage.Is there enough oil beneath the Arctic National Wildlife Refuge (保护区) (ANWR) to help secure America’s energy future? President Bush certainly thinks so. He has argued that tapping ANWR’ s oil would help ease California’s electricity crisis and provide a major boost to the country’s energy independence. But no one knows for sure how much crude oil lies buried beneath the frozen earth, with the last government survey, conducted in1998, projecting output anywhere from 3 billion to 16 billion barrels.The oil industry goes with the high end of the range, which could equal as much as 10% of U.S. consumption for as long as six years. By pumping more than 1 million barrels a day from the reserve for the next two to three decades, lobbyists claim, the nation could cut back on imports equivalent to all shipments to the U.S. from Saudi Arabia. Sounds good. An oil boom would also mean a multibillion-dollar windfall (意外之财) in tax revenues, royalties (开采权使用费) and leasing fees for Alaska and the Federal Government. Best of all, advocates of drilling say, damage to the environment Would be insignificant. “We’ve never had a documented case of an oil rig chasing deer out onto thepack ice,” say Alaska State Representative Scott Ogan.Not so fast, say environmentalists. Sticking to the low end of government estimates the National Resources Defends Council says there may be no more than 3.2 billion barrels of economically recoverable oil in the coastal plain of ANWR, a drop in the bucket that would do virtually nothing to ease America’s energy problems. And consumers would wait up to a decade to gain any benefits, because drilling could begin only after mush bargaining over leases, environmental permits and regulatory review.As for ANWR’s impact on the California power crisis, environmentalists point out that oil is responsible for only 1% of the Golden State’s electricity output ---and just 3% of thenation’s.Directions: In this section there are three passages. Each passage is followed by some questions or unfinished statements with four choices marked [A], [B], [C], and [D]. You are supposed to read the passage and make the best choice to complete each question or unfinished statement.Question 21 to 25 are based on the following passage.Is there enough oil beneath the Arctic National Wildlife Refuge (保护区) (ANWR) to help secure America’s energy future? President Bush certainly thinks so. He has argued that tapping ANWR’ s oil would help ease California’s electricity crisis and provide a major boost to the country’s energy independence. But no one knows for sure how much crude oil lies buried beneath the frozen earth, with the last government survey, conducted in1998, projecting output anywhere from 3 billion to 16 billion barrels.The oil industry goes with the high end of the range, which could equal as much as 10% of U.S. consumption for as long as six years. By pumping more than 1 million barrels a day from the reserve for the next two to three decades, lobbyists claim, the nation could cut back on imports equivalent to all shipments to the U.S. from Saudi Arabia. Sounds good. An oil boom would also mean a multibillion-dollar windfall (意外之财) in tax revenues, royalties (开采权使用费) and leasing fees for Alaska and the Federal Government. Best of all, advocates of drilling say, damage to the environment Would be insignificant. “We’ve never had a documented case of an oil rig chasing deer out onto the pack ice,” say Alaska State Representative Scott Ogan.Not so fast, say environmentalists. Sticking to the low end of government estimates the National Resources Defends Council says there may be no more than 3.2 billion barrelsof economically recoverable oil in the coastal plain of ANWR, a drop in the bucket that would do virtually nothing to ease America’s energy problems. And consumers would wait up to a decade to gain any benefits, because drilling could begin only after mush bargaining over leases, environmental permits and regulatory review.As for ANWR’s impact on the California power crisis, environmentalists point out that oil is responsible for only 1% of the Golden State’s electricity output ---and just 3% of the nation’s.21. What does President Bush think of tapping oil in ANWR? [单选题]A It will increase America’s energy consumption.B It will exhaust the nation’s oil reserves.C It will help reduce the nation’s oil imports.(正确答案)D It will help secure the future of ANWR.22. We learn from the second paragraph that the American oil industry _________. [单选题]A shows little interest tapping oil in ANWRB) expect to stop oil imports from Saudi ArabiaC) tend to exaggerate America’s reliance on foreign oilD) believes that drilling for ANWR will produce high yields(正确答案)23. Those against oil drilling ANWR argue that ________. [单选题]A it will drain the oil reserves in the Alaskan regionB) it can do little to solve U.S. energy problem(正确答案)C it can cause serious damage to the environmentD it will not have much commercial value24. What do the environmentalists mean by saying “Not so fast” (Line1, Psra.3)? [单选题]A Don’t be too optimistic.(正确答案)B Don’t expect fast returns.C The oil drilling should be delayed.D Oil exploitation takes a long time.25. It can be learned from the passage that oil exploitation beneath ANWR’s frozen earth ________. [单选题]A) involves a lot of technological problemsB) remains a controversial issue(正确答案)C) is expected to get under way soonD) will enable the U.S. to be oil independentQuestion 26 to 30 are based on the following passage.“Tear’em apart!”“Kill the fool!”“Murder the referee(裁判) !”These are common remarks one may hear at various sporting events. At the time they are made ,they may seem innocent enough. But let’s not kid ourselves .They have been known to influence behavior in such a way as to lead to real bloodshed. Volumes have been written about the way word affect us. It has been shown that words having certain connotations (含义) may cause us to react in ways quite foreign to what we consider to be our usual humanistic behavior. I see the term “opponent” as one of thosewords .Perhaps the time has come to delete it from sports terms.The dictionary meaning of the term “opponent” is “adversary”;“enemy”“one who opposes your interests. ”Thus, when a player meets an opponent ,he or she may tend to every action no matter how gross ,may be considered justifiable. I recall an incident in a handball game when a referee refused a player’s request for a time out for a glove change because he did not consider them wet enough .The player proceeded to rub his gloves across his wet T-shirt and then exclaimed, “Are they wet enough now?”In the heat of battle, players have been observed to throw themselves across the courtwithout considering the consequences the such a move might have on anyone in their way. I have also witnessed a player reacting to his opponent’s intentional and illegal blocking by deliberately hitting him with the ball as hard as he could during the course of play. Off the court, they are good friends. Does that make any sense? It certainly gives proof of a court attitude which departs from normal behavior.Therefore, I believe it is time we elevated (提升) the game to the level where it belongs, thereby setting an example to the rest of the sporting world. Replacing the term “opponent” with “associate” could be an ideal way to start.The dictionary meaning of the term “associate” is “colleague”;“friend”;“companion.”Reflect a moment! You may soon see and possibly feel the difference in your reaction to the term “associate” rather than “opponent”.26. Which of the following statements best expresses the author’s view? [单选题]A The words people use can influence their behavior.(正确答案)B Unpleasant words in sports are often used by foreign athletes.C Aggressive behavior in sports can have serious consequences.D Unfair judgments by referees will lead to violence on the sports field.27. Harsh words are spoken during games because the players_______. [单选题]A are too eager to winB treat their rivals as enemies(正确答案)C are usually short-tempered and easily offendedD cannot afford to be polite in fierce competitions28. What did the handball player do when he was not allowed a time out to change his gloves? [单选题]A He angrily hit the referee with a ball.B He refused to continue the game.C He claimed that referee was unfair.D He wet his gloves by rubbing them across his T-shirt.(正确答案)29. According to the passage, players in a game may______. [单选题]A kick the ball across the court with forceB lie down on the ground as an act of protestC deliberately throw the ball at anyone illegally blocking their way(正确答案)D keep on screaming and shouting throughout the game30. The author hopes to have the current situation un sports improved by ________. [单选题]A regulating the relationship between players and refereesB calling on players to use clean language in the courtC raising the referee’s sense of responsibilityD changing the attitude of players on the sports field(正确答案)四、完形填空（每小题1 分，共15分）A new study found that inner-city kids living in neighborhoods with more green space gained about 13% less weight over a two-year period than kids living amid more concrete and fewer trees. Such __36__ tell a powerful story. The obesity epidemic began in the 1980s, and many people __37__ it to increased portion sizes and inactivity, but that can't be everything. Fast foods and TVs have been __38__ us for a long time. "Most experts agree that the changes were __39__ to something in the environment," says social epidemiologist Thomas Glass of The Johns Hopkins Bloomberg School of Public Health. That something could be a __40__ of the green.The new research, __41__ in the American Journal of Preventive Medicine, isn't thefirst to associate greenery with better health, but it does get us closer __42__ identifying what works and why. At its most straightforward, a green neighborhood __43__ means more places for kids to play – which is __44__ since time spent outdoors is one of the strongest correlates of children's activity levels. But green space is good for the mind__45__: research by environmental psychologists has shown that it has cognitive __46__ for children with attention-deficit disorder. In one study, just reading __47__ in a green setting improved kids' symptoms.__48__ to grassy areas has also been linked to __49__ stress and a lower body mass index (体重指数) among adults. And an __50__ of 3,000 Tokyo residents associated walkable green spaces with greater longevity (长寿) among senior citizens.31.选择对应单词 [单选题]A.findings(正确答案)B thesesC) hypothesesD) abstracts32. 选择对应单词 [单选题]A.adaptB. attribute(正确答案)C.allocateD. alternate33. 选择对应单词 [单选题]A.amongstB.alongC.besideD.with(正确答案)34选择对应单词 [单选题]A .gluedB.related(正确答案)C)trackedD . appointed35.选择对应单词 [单选题]A. scrapingB. denyingC. depressingD. shrinking(正确答案)36.选择对应单词 [单选题]A .published(正确答案)B. simulatedC.illuminatedD. circulated37.选择对应单词 [单选题]A. atB. to(正确答案)C. forD. over38. 选择对应单词 [单选题]A. fullyB. simply(正确答案)C. seriouslyD. uniquely39. 选择对应单词 [单选题]A. vital(正确答案)B. casualC. fatalD. subtle40. 选择对应单词 [单选题]A. stillB. alreadyC. too(正确答案)D. yet41. 选择对应单词 [单选题]A. benefits(正确答案)B. profitsC. revenuesD. awards42. 选择对应单词 [单选题]A. outwardB. apartC. asideD. outside(正确答案)43. 选择对应单词 [单选题]A. ImmunityB. ReactionC. Exposure(正确答案)D. Addiction44. 选择对应单词 [单选题]A. muchB. less(正确答案)C. moreD. little45. 选择对应单词 [单选题]A. installmentB. expeditionC. analysis(正确答案)D. option五、英汉翻译（每小题4分，共32分）46. 与申请这个职位的其他女孩相比，她流利的英语是个优势。