A Non-Parametric Bayesian Approach to Spike Sorting

What do the headers in the table mean?∙Src = source code included? (N=no) If so, what language?∙API = application program interface included? (N means the program cannot be integrated into your code, i.e., it must be run as a standalone executable.)∙Exec = Executable runs on W = Windows (95/98/NT), U = Unix, M = Mac, or - = any machine with a compiler.∙Cts = are continuous (latent) nodes supported? G = (conditionally) Gaussians nodes supported analytically, Cs = continuous nodes supported by sampling, Cd = continuous nodes supported by discretization, Cx = continuous nodes supported by some unspecified method, D = only discrete nodes supported.∙GUI = Graphical User Interface included?∙Learns parameters?∙Learns structure? CI = means uses conditional independency tests∙Utility = utility and decision nodes (i.e., influence diagrams) supported?∙Free? 0 = free (although possibly only for academic use). $ = commercial software (although most have free versions which are restricted in various ways, e.g., the model size is limited, or models cannot be saved, or there is no API.)∙Undir? What kind of graphs are supported? U = only undirected graphs, D = only directed graphs, UD = both undirected and directed, CG = chain graphs (mixed directed/undirected).∙Inference = which inference algorithm is used? jtree = junction tree, varelim = variable (bucket) elimination, MH = Metropols Hastings, G = Gibbs sampling, IS = importance sampling, sampling = some other Monte Carlo method, polytree = Pearl's algorithm restricted to a graph with no cycles, VMP = variational message passing, EP = expectation propagation, SL = the program is designed for structure learning from completely observed data, not state estimation ∙Comments. If in "quotes", I am quoting the authors at their request.。

By members & collaborators of the Wellcome Trust Centre for Neuroimaging Introduction| Software | Documentation | Courses | Email list | Data |ExtensionsSPM Menu:Introduction Software Documentation Courses Email list Data setsExtensionsThis page:Introduction Getting started Latest news SPM in briefStatistical Parametric Mapping IntroductionStatistical Parametric Mapping refers to the construction and assessment of spatially extended statistical processes used to test hypotheses about functional imaging data. These ideas have been instantiated in software that is called SPM.The SPM software package has been designed for the analysis of brain imaging data sequences. The sequences can be a series of images from different cohorts, or time-series from the same subject. The current release is designed for the analysis of fMRI,PET, SPECT, EEG and MEG.Getting StartedThe best starting point is to read the introductory article on SPM available here. You could then download the latest version of the software and a data set to analyse. Step-by-step instructions for this analysis are available in the SPM manual.If you're new to imaging, perhaps an epoch fMRI data set would be appropriate. The data sets are provided with instructions on how to use SPM to analyse them. These tutorials therefore give practical instructions on how to implement the various methodologies. Our methods have been written up in books, technical reports and journal papers which are available from our Online Bibliography. This groups documentation according to year, category, author and keyword.If you're looking for help on a particular topic you can find the relevant papers from the Online Bibliography. Alternatively, you can search the SPM pages using the search facility that appears at the bottom of every page. Also browse and search the SPM WikiBook and please feel free to edit it if you can. If you still can't find what you need, you could send an email to the SPM Email list, which gives you access to our community of experts.You should also be aware of the many courses on SPM. If there isn't one in your country this year then there's always the annual short course in London. Finally, once you've mastered SPM you can learn about the various extensions provided by experts in the wider community.Good luck !Latest newsSPM Course for M/EEG VideosJuly 2012: Videos recorded at the May 2012 SPM Course for M/EEG are now freely available online.SPM Course for fMRI/PET/VBM VideosNovember 2011: Videos recorded at the May 2011 SPM Course for fMRI/PET/VBM are now freely available online.SPM8 releasedApril 2009: SPM8 is a major update to the SPM software, containing substantial theoretical, algorithmic, structural and interface enhancements over previous versions (more info).New Book: Statistical Parametric Mapping: TheAnalysis of Functional Brain ImagesNovember 2006: This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography (more info).The SPM approach in briefThe Statistical Parametric Mapping approach is voxel based:∙Images are realigned, spatially normalised into a standard space, and smoothed.∙Parametric statistical models are assumed at each voxel, using the General Linear Model GLM to describe the data in terms of experimental and confounding effects, and residual variability.∙For fMRI the GLM is used in combination with a temporal convolution model.∙Classical statistical inference is used to test hypotheses that are expressed in terms of GLM parameters. This uses an image whose voxel values are statistics, a Statistic Image, or Statistical Parametric Map (SPM{t}, SPM{Z}, SPM{F})∙For such classical inferences, the multiple comparisons problem is addressed using continuous random field theory RFT, assuming the statistic image to be a good lattice representation of an underlying continuous stationary random field. This results in inference based on corrected p-values.∙Bayesian inference can be used in place of classical inference resulting in Posterior Probability Maps PPM s.For fMRI, analyses of effective connectivity can be implemented using Dynamic Causal Modelling DCM.Last modified $Date: 2013/06/24 19:14:39 $ by $Author: guillaume $ home | search | sitemapCopyright © 1991,1994-2013 FILT SoftwareIntroductionSPM is made freely available to the [neuro]imaging community, to promote collaboration and a common analysis scheme across laboratories. The software represents the implementation of the theoretical concepts of Statistical Parametric Mapping in a complete analysis package.The SPM software is a suite of MATLAB (The MathWorks, Inc) functions and subroutines with some externally compiled C routines.SPM was written to organise and interpret our functional neuroimaging data. The distributed version is the same as that we use ourselves.LicenceSPM is free but copyright software, distributed under the terms of the GNU General Public Licence as published by the Free Software Foundation (either version 2, as given in file spm_LICENCE.man, or at your option, any later version). Further details on "copyleft" can be found at /copyleft/. In particular, SPM is supplied as is. No formal support or maintenance is provided or implied.Beta version: SPM12bA beta version of SPM12, SPM12b, was released 21st December 2012 and is available for beta-testing. Please assist us by reporting bugs to <fil.spm@>.Current version: SPM8The current version is SPM8and was released inApril 2009. This provides a major update to theSPMsoftware, containing substantial theoretical,algorithmic, structural and interface enhancementsover previous versions.SPM8 uses the NIfTI-1 file format.Previous versionsWe still provide access to previous versions of SPM, but recommend you use the current version wherever possible.SPM5SPM5 was released in December 2005.SPM2SPM2 was released in 2003.SPM99SPM99was released in January 2000.SPM96 and earlier versions are no longer available.NITRCSPM is listed in the Neuroimaging Informatics Tools andResources Clearinghouse (NITRC ). See /projects/spm/. Funded by the NationalInstitutes of Health Blueprint for Neuroscience Research,NITRC facilitates finding and comparing neuroimagingresources for fMRI and related structural analyses.Last modified $Date: 2014/02/27 12:08:57 $ by $Author: guillaume $ home | search | sitemapCopyright © 1991,1994-2014 FILThe FIL Methods group <fil.spm@ >he FIL Methods group <fil.spm@ > Documentation IntroductionSPM is an academic software toolkit for the analysis of functional imaging data, for users familiar with the underlying statistical, mathematical and image processing concepts. It is essential to understand these underlying concepts in order to use the software effectively. A good starting point is the Introduction to SPM, by Karl Friston.Peer reviewed literatureThe primary reference for the theories underlying SPM are the academic papers in the peer reviewed literature. These are available via the Online Bibliography which organises books, papers and technical reports by year, category, author and keyword. An Annotated Bibliography provides a guide to the various papers.BooksThe book Statistical Parametric Mapping: The Analysis ofFunctional Brain Images (2007) provides the backgroundand methodology for the analysis of all types of brainimaging data, from functional magnetic resonanceimaging to magnetoencephalography. Critically,"Statistical Parametric Mapping"provides a widelyaccepted conceptual framework which allows treatmentof all these different modalities. The book takes thereader from the basic concepts underlying the analysis ofneuroimaging data to cutting edge approaches thatwould be difficult to find in any other source. The materialis presented in an incremental way so that the reader canunderstand the precedents for each new development.This book will be particularly useful to neuroscientistsengaged in any form of brain mapping; who have tocontend with the real-world problems of data analysisand understanding the techniques they are using. It isprimarily a scientific treatment and a didactic introductionto the analysis of brain imaging data. It can be used asboth a textbook for students and scientists starting to usethe techniques, as well as a reference for practicingneuroscientists.The book can be ordered online via Elsevier or, e.g., Amazon.Introductory articles are also provided in the earlier book Human Brain Function. PDFs of draft versions of book chapters are available online: ∙First Edition(1997)∙Second Edition(2003)ManualThere is an SPM8 manual distributed with the software (spm8/man/manual.pdf), which is written by the developers. Much of the manual's contents are also available via the SPM8 user-interface.The release notes accompanying SPM8 contain some useful information.The SPM5 distribution also contains a manual in (spm5/man/manual.pdf). There is no manual for SPM2, but the SPM99 manual is roughly applicable. Methods for DummiesEach year our department runs a series of methods talks by non-experts. Powerpoint versions are available for 2003, organised by Alexa Morcom, 2004, organised by Lucy Lee, 2005, orgainsed by Julia Hocking, 2006, organised by Davina Bristow and Marcus Gray,2007, organised by Justin Chumbley and Hanneke den Ouden,2008 organised by Maria Joao, Hanneke den Ouden and Justin Chumbley,2009organised by Antoinette Nicolle and Maria Joao,2010 organised by Christian Lambert, Suz Prejawa and Maria Joao, and 2011 organised by Rumana Chowdhury, Peter Smittenaar and Suz Prejawa. This years meetings are organised by Mona Gavert, Peter Smittenaar and Giles Story.Third party documentationThere is a SPM WikiBook, which is written and maintained by the international SPM community. The wiki allows users to read and edit the content for free. The end results will be mature, up-to-date and broad repositories for information on SPM. Please do take a look at the SPM wiki and feel free to contribute to it if you can.SPM WikiBooks/wiki/SPMBeginners guides & overviews of SPM :Cambridge Imaging Home Page (MRC Cognition and Brain Sciences Unit) /imagingHistoryThe SPM suite and associated theory was originally developed by Karl Friston for the routine statistical analysis of functional neuroimaging data from Positron Emission Tomography (PET), while at the Medical Research Council Cyclotron Unit. Now known as SPM classic, this software was made available to the emerging functional imaging community in 1991, to promote collaboration and a common analysis scheme across laboratories.SPM'94 was the first major revision of the SPM software. SPM'94 was written primarily by Karl Friston during the summer of 1994, with invaluable conceptual and technical help from John Ashburner, Jon Heather, Andrew Holmes and Jean-Baptiste Poline. SPM'95, SPM'96, SPM'99, SPM2, SPM5 and SPM8are based on SPM'94, and represent the ongoing theoretical advances and technical improvements.Tell me more about SPM history.Last modified $Date: 2013/01/22 11:55:27 $ by $Author: spm $home | search | sitemapCopyright © 1991,1994-2013 FILThe FIL Methods group <fil.spm@>SPM CoursesLondon, May & October 2014The FIL SPM course on using Statistical Parametric Mapping for neuroimaging is held each May and October as part of the Institute of Neurology's short course programme.Since 2010, we provide two separate SPM courses reflecting the different imaging modalities. There is a new three-day course on SPM for EEG/MEG followed by the long-established three-day course on SPM for fMRI/VBM/PET. Both courses are suitable for beginners and more advanced users. We advise students to gain at least some minimal familiarity with the methodology, for example, from reading introductory articles available from the SPM web pageor by following data analysis examples in the SPM manual.The next SPM courses in London will take place on 12-14 May 2014 (MEG/EEG) and 15-17 May 2014 (MRI/VBM/fMRI).The courses are organised through the Institute of Neurology(contact: Miss Jean Reynolds at the IoN to register).Externally organised SPM coursesOther SPM courses are organised around the world at different times of year and in different languages. If you do organise one, please let us know so that it can be listed here.Lausanne SPM Course, Switzerland, 22-25 April 2014This 6th edition of the Lausanne SPM course will focus on how to conduct neuroimaging studies using structural and functional MRI data within the framework of Statistical Parametric Mapping (SPM). This 4 days course is divided into two modules with theoretical and practical sessions covering all aspects of imaging data analysis from spatial pre-processing to statistical inference and reporting results. The course is suitable both for beginners and for those with previous experience of SPM.http://www3.unil.ch/wpmu/lren-spm/Zurich SPM course, Switzerland, 2015This three-day course, which is held annually since 2007, offers a comprehensive coverage of all MRI-related aspects of SPM./spm-course-2014/Course material for 2008, 2009, 2010, 2011, 2012, 2013, 2014Hannover SPM course, Germany, 3-4 November 2014The 7th SPM workshop for Beginners in Hannover, Germany, will be held on November 03. and 04. 2014. (teaching language: german)More information and program:http://www.spmworkshop-hannover.de/SPM Workshops at the Martinos Center, Boston, Massachusetts, USA: /martinos/training/fMRI-Extension/SPM8.phpMRN fMRI Image Acquisition and Analyses Course, University of Colorado, Boulder, USA:/courses/Slides of previous coursesThe latest course material are from 2013 (fMRI/VBM) and 2013 (MEEG).Archive:2002, 2003, 2004, 2005, 2005 (USA), 2006, 2007, 2008 (May), 2008 (October), 2009 (May), 2009 (October), 2009 (MEEG), 2010 (fMRI), 2010 (MEEG), 2010 (Vancouver), 2010 (October), 2011 (Brussels)May 2011 (fMRI), May 2011 (MEEG), Oct 2011 (fMRI), 2012 (MEEG, Lyon), May 2012 (fMRI/VBM), 2012 (MEEG), Oct 2012 (fMRI/VBM), May 2013 (fMRI/VBM).These can be viewed using the Microsoft PowerPoint Viewer for Windows or the multi-platform Open Office.RecordingsOnline videos are now available, recorded at the May 2011 SPM for fMRI/PET/VBM course and at the May 2012 SPM for MEG/EEG course. Higher quality versions of the videos can be obtained on a DVD available for purchase.Last modified $Date: 2014/02/26 16:06:03 $ by $Author: guillaume $ home | search | sitemapCopyright © 1991,1994-2014 FILThe FIL Methods group <fil.spm@>Discussion ListIntroductionThe SPM discussion list is an electronic mailing list for discussion and help with the methodology, implementation and use of Statistical Parametric Mapping and the SPM package. The list is not moderated, but is monitoredand owned by members of the Wellcome Trust Centre for Neuroimaging. Much of the approach and use of SPM is described in the documentation. Subscribers are urged to consult these sources, and any local expertise, before using the discussion list as a helpline. A response from one of the SPM authors cannot be guaranteed, due to resource limitations. Experienced list members are therefore encouraged to address issues within their experience, posting their responses & discussion to the list for general enlightenment.Searching archives∙Archives of SPM messages.∙Search SPMarchives.SubscriptionThe list is run at the UK's automated JISCmail service.To subscribe or unsubscribe to the SPM list:Enter your details at /cgi-bin/webadmin?SUBED1=spm&A=1To send a message to all the people currently subscribed to the SPM list: Just send a mail to <spm@> after subscription.If you have difficulties, then have a look to the frequently asked questions about JISCmail or email the list owner at <fil.spm@>, for assistance. Last modified $Date: 2013/01/22 11:55:31 $ by $Author: spm $home | search | sitemapCopyright © 1991,1994-2013 FILThe FIL Methods group <fil.spm@>Data sets and tutorialsIntroductionThe following data sets are being made available for training and personal education and evaluation purposes. Those wishing to use these data for other purposes, including illustrations or evaluations of methods, should contact the Methods group at the Wellcome Trust Centre for Neuroimaging.A set of instructions showing how SPM can be used to analyse each data set are also provided. These tutorials show how one can use SPM to implement analyses of PET data, epoch or event-related fMRI data, and data from a group of subjects using Random effects analyses (RFX). They also cover more advanced topics such as Psychophysiological Interactions (PPI s) and Dynamic Causal Modelling (DCM).fMRI: epochThe instructions accompanying these data sets show you how to implement a block-design fMRI analysis in SPM. They are both single-subject or 'first-level' analyses.∙Auditory - single subject∙Attention to Visual Motion - single subjectThe instructions accompanying the Attention to Visual Motion data also show you how to use SPM to implement, for example, Psychophysiological Interactions (PPI s) and Dynamic Causal Modelling (DCM).fMRI: event-relatedThe instructions accompanying these data sets show you how to use SPM to analyse data for an event-related fMRI experiment. This includes, for example, selection of different temporal basis sets. They are both single-subject or 'first-level' analyses.∙Repetition primingfMRI: multi-subject (random effects) analyses These data sets comprise contrast images from single-subject fMRI analyses or 'first-level' analyses from the repetition priming experiment described here.In the summary statistic approach to Random Effects Analysis (RFX) these contrast images are then used in a 'second-level' analysis allowing you to make inferences about the population from which the subjects were drawn.∙fMRI: multi-subject (random effects) analysesfMRI: Bayesian comparison of DCMsDynamic Causal Models from an event related fMRI study of the language system are available here∙fMRI: Bayesian comparison of DCMsEEG Single Subject Mismatch Negativity datasetThis is an 128-channel EEG single subject example data set which is used for demonstrating the usage of scripts in M/EEG pre-processing and DCM for evoked responses.Anaesthesia Depth in Rodent DataThis 2-channel Local Field Potential (LFPs) dataset demonstrates the use of DCM for Cross Spectral Densities.Multi-modal facesThis archive contains EEG, MEG and fMRI data on the same subject within the same paradigm.It can be used to examine how various measures of face perception, such as the "N170" ERP (EEG), the "M170" ERF (MEG) and fusiform activation (fMRI), are related. For example, the localisation of the generator(s) of the N170 and/or M170 can be constrained by the fMRI activations.It also includes a high resolution anatomical MRI image (aMRI) for construction of a head-model for the EEG and MEG data, together with data from a Polhemus digitizer that can be used to coregister the EEG and MEG data with the aMRI.FieldMapHere are two example data sets that can be used to demonstrate the usage of the FieldMap toolbox.PETThe instructions accompanying these data sets show you how to use SPM to analyse PET data.∙Verbal fluency - multiple subjects∙Motor activation - single subjectLast modified $Date: 2014/04/30 17:48:34 $ by $Author: guillaume $ home | search | sitemapCopyright © 1991,1994-2014 FILThe FIL Methods group <fil.spm@>SPM ExtensionsIntroductionMany SPM users have created tools for neuroimaging analyses that are based on SPM. You will find here a list of these tools classified between Toolboxes, Utilities, Batch Systems and Templates. The distinction between Toolboxes and Utilities can be blurry, but for the purposes of this page we define a toolbox to be a utility that can be completely operated via a graphical user interface.If you notice inaccuracies or out of date links, please email the SPM manager. Likewise, to have your SPM extension linked here, send an email including a URL, a contact email, and a brief summary (please note if any MATLABtoolboxes are required, or if it is platform-specific).The SPM Developers take no responsibility for the usability of the extensions listed here. In particular, some extensions may be mutually incompatible. Please contact the respective extension authors with questions and problems (though CC'ing answered questions to the Email list will be appreciated).Extensions compatible with SPM8, SPM5, SPM2, SPM99.The list of SPM extensions is also available as an RSS feed.Note: All email addresses in this page have their "@" replaced with "_at_" to minimize spam. Please reverse this change before emailing.Quick LinksToolboxes:AQuA | AAL | ACID | ALVIN | ArtRepair | AMAT | AnalyzeMovie | Anatomy | aslm | ASLtbx | at4fmri | aws4SPM | BrainNetViewer | BredeQuery | CCAfMRI | CLASS| Clinical| Complexity| conn| CPCA| DAiSS| DICOMCD_Import| Diffusion_II | Distance | DPARSF | DRIFTER | EMS | ExtractVals | FASL | FAST | FDR | FieldMap | fieldmap_undistort | FieldTrip | fMRIPower | fOSA | Grocer | HRF | HV | IBASPM | iBrainAT | iBrainLT | INRIAlign | IBZM_tool | ISAS | LI | LogTransform | MARINA | MarsBar | MASCOI | mfBox | Masking | Masks | MM | multifocal | NIRS-SPM | NS | Ortho | PSPM | REST | rfxplot | RobustWLS | SCRalyze| SDM| SimpleROIBuilder| SnPM| spm_wavelet| SPMd| SPMMouse| SSM| SUIT| SurfRend| TOM| UF2C| Unwarp2| Volumes| WBM | WSPM | WFU_PickAtlas | xjView | XMLToolsUtilities:AveLI| BrainMagix| Bruker2Analyze| CBMG-Tools| Design_Magic| dicom2nifti| DynPET| Easy_ROI| Easy_Volumes| FDRill| Fluctuation| fToolbelt| FAD| GA| GE2SPM| GIFT| JG| L2S| log_roi_batch| LMGS| Motion| mri_toolbox| MSU| Orth1| PCT| pvconv| r2agui| SEM| slice_overlay | TSDiffAna | TSU | iTT | VBMtools | VIS | visionToSPM | VoiTool Batch Utilities:aa| AutoSPET| BatchAAL| KULscripts| parallelize_matlabbatch| spm_segment | spm2-batch | spm2batch | spm2Batch | spmbatch | spmjob | X_batch | zephyrTemplates:Baboon| BrainDev_Atlas| Cerebellum| CCHMC_Pediatric| Macaca_Fascicularis| Macaca_Fascicularis_PET| Macaca_Mulatta| Macaca_Nemestrina | Rat | SPMtemplates | UNC_Pediatric | Zebra_FinchToolboxesAQuA SPM5Summary: AQuA is a tool that helps you in the assessment process for the quality of the acquired fMRI data, identifying images with movement and other artefacts, so that they do not compromise the experimental analysis. Author: Antonios Antoniou and Juan J. LullURL: http://www.ibime.upv.es/mi/AAL - Anatomical Automatic Labeling SPM99 SPM2 SPM5 SPM8Summary: Automated parcellation method, as described in Tzourio-Mazoyer et al. NI 2002.Author: CyceronURL: rs.fr/spip.php?article217ACID - Artefact correction in diffusion MRI SPM8 Summary: The Artefact correction in diffusion MRI (ACID) toolbox is an academic software toolkit for pre-processing of diffusion MRI data, estimation of DTI indices and normalisation of DTI index maps, which fully integrates into the batch system of SPM8.Author: Siawoosh MohammadiURL: /ALVIN - Automatic Lateral Ventricle delIneatioNSPM8Summary: Segmentation of the lateral ventricles validated in infants, adults and patients with Alzheimer's disease. Works with both T1 and T2 images. Author: Matthew KemptonURL: /site/mrilateralventricle/ArtRepair - Artifact Repair toolbox SPM2 SPM5 SPM8Summary: Special methods to improve the fMRI analysis of high motion pediatric and clinical subjects. The methods correct for large motions, and automatically detect and remove artifact noise in the data. Viewing tools allow quality checking at every step in the analysis.Author: Paul MazaikaURL:/tools/human-brain-project/artrepair-software.html AMAT: A meta-analysis toolbox SPM2Summary: AMAT is a matlab program which lets you search through the coordinates reported in lots of fMRI papers. It is designed to answer the frequently asked question: what the *?%! does that bit do?Author: Antonia HamiltonURL: /amat.htmlAnalyzeMovie - AVI movies from Analyze images SPM99Summary: Create AVI movies from Analyze images, of axial, coronal, sagittal or ortho slices. Requires Matlab6 or greater.Author: Robert WelshURL: /ni-stat/AnalyzeMovie.tarAnatomy - SPM Anatomy toolbox SPM99 SPM2 SPM5 SPM8Summary: This toolbox integrates probabilistic cytoarchitectonic maps derived from human post-mortem studies into the SPM environment and provides a wide range of different approaches to analyse structure / function correlations.Author: Simon EickhoffURL:http://www.fz-juelich.de/inm/inm-1/DE/Forschung/_docs/SPMAnatomyToolbox /SPMAnatomyToolbox_node.htmlaslm - a slightly modified asl-module SPM8 Summary: aslm is an object orientated toolbox for common tasks associated with the analysis of arterial spin labeling (ASL) and other MRI data.Author: Philipp HomanURL: ASLtbx SPM2 SPM5 SPM8Summary: ASLtbx is a Matlab and SPM based toolkit for processing arterial spin labeling (ASL) perfusion MRI data. It's basically a collection of a bunch of batch scripts. I'm currently only distributing the SPM5-based version, but the SPM2(or 8)-based version can be obtained through email. The function for quantifying cerebral blood flow should be SPM independent except the image reading and writing functions from SPM.Author: Ze WangURL: /~zewang/ASLtbx.phpat4fmri - adaptive thresholding of fMRI maps SPM8 Summary: Allow to obtain a threshold for cluster FDR - the method fits a Gamma-Gaussian mixture model to the SPM-T and finds the optimal threshold(crossing between noise and activation). Optionally write the thresholded maps.Author: Chris Filo Gorgolewski and Cyril PernetURL: /projects/at-4-fmri/aws4SPM SPM2 SPM5 SPM8Summary: Structural adaptive smoothing fMRI data as described in Tabelow et al. NI (2006).Author: Devy Hoffmann and Karsten TabelowURL: http://www.wias-berlin.de/software/aws4SPM/BrainNet ViewerSummary: BrainNet Viewer is a brain network visualization tool, which can help researchers to visualize structural and functional connectivity patterns from different levels in a quick, easy, and flexible way.Author: Mingrui XiaURL: /projects/bnv/BredeQuery SPM5Summary: BredeQuery plugin for SPM5 - enables coordinate-based meta-analytic search of related literature for brain regions directly from SPM5 environment. The coordinate-based search is performed using Finn Aarup Nielsen's Brede Database. Works with coordinates in Talairach and MNI space, MNI-to-Talairach transformations are available (Brett and Lancaster transformations). Moreover, query results can be exported automatically to the suitable bibliographic file format (BibTeX, Reference Manager, RefWorks, EndNote).Author: Bartlomiej WilkowskiURL: http://neuro.imm.dtu.dk/wiki/BredeQueryCCA-fMRI SPM2 SPM5Summary: The CCA-fMRI utilizes canonical correlation analysis in combination with the Balloon model and adaptive filtering of fMRI data to detect areas of brain activation. The CCA-fMRI toolbox provides its own user interface and can also be used as stand alone scripts, e.g. for batch processing.Author: Magnus BorgaURL: /CLASS - Classifier Learning for Asymmetrically Small Samples SPM8Summary: Multivariate kernel-based pattern classification using support vector machines (SVM) with a novel modification to obtain more balanced sensitivity and specificity on unbalanced data-sets (i.e. those with very different numbers of cases in each group).Author: Ged RidgwayURL: Contact email aboveClinical Toolbox SPM8Summary: Aids normalization of clinical scans, providing an easy way to include lesion cost function masking. Allows unified segmentation-normalization (USN) or traditional normalization. Includes custom age adjusted templates for CT/CAT scans and USN. Includes FLAIR template provided by the Glahn group.Author: Rorden, Bonilha, Fridriksson, Bender and KarnathURL: /CRNL/clinical-toolbox Complexity SPM8Summary: Complexity is a toolkit used to analyze the complexity of resting state fMRI (rs-fMRI) data. Pre-processing module is included to realize low pass filtering and linear detrending. Five methods, Approximate Entropy, Sample Entropy, Cross Approximate Entropy, Multiscale Sample Entropy and Wavelet MSE, are available to calculate the entropy. Matlab toolbox, "Tools for NIfTI and ANALYZE image", is needed.。

Chapter 5 Estimation and LearningOutline■Parametric EstimationMaximum Likelihood Estimation Unbiased Estimates Bayes Estimation■Non-Parametric EstimationHistogram EstimationParzen Window Estimation A^Neares十・Neighbour EstimationEstimationa. Parameter estimation - assume a known form for the p.d.f. and estimate the necessary parameters (mean and variance for normalb. Density estimation ・ estimate the non-parametric pdf Js from the given samples.Maximum Likelihood method•Parameters are viewed as unknown but fixed valuesBavesian method Learning or Maximum u Poerteriori Estimation.•Parameters are random variables that have their distributionsA conmion assumption ・Gaussian e = (nQ/ \ ' --------------------- " -------- ?Number of "Volume^ Squareddimensions of the Malialanobiscova rianc e dist anc e= £ x]d parameters工二E[(«X -”)厂(X_#)d(d + 1)/2 parameterso「1 0 .5_LI =0 V - 0 1 .30 .5 .3 1 Constant density, (x - ")厂工"(x —")二 C - quadratic surfaceE - Positive semidefiniteellipsoidPrincipal axes: eigenvectors of X Length:丽」A ■ eigenvalues of ZWhitening TransformA = diag^eigval（工））①=eigvec（工）Then:W = AFor all:-Scaling matrix-Rotation matrix-4t Unscales^ and 4'unrotate the data倏~N（0J）§5・1.1 Maximum Likelihood EstimationParameters are fixed but unknown.D 三|・ a data set, drawn from p(x)Notationally, we make density explicitly dependent on parameters:贸凶10)Figure 5.1: Given an obsenation 船」he maximum likelihood estimate of parameter 0 is chosen co be that value which maximizes the PDF 卩（壬』0）・§5・1.1 Maximum Likelihood EstimationP(x)二p(“ |&)Assuming that the data is drawn independently (i.i.d.):N-a likelihood furictiori ue^P(D\e)= Yfp(x f1\e)77=1To find 0 Maximize Z(0 ) w.r.t. parameters.§5・1.1 Maximum Likelihood Estimation Maximizing Z（9 ） is equivalent to maximizing log-likelihoodfiinctiori:N N«0）三log 厶（e）= iog「［p（x" |8）=工iogp（* |e）77=1 n=lTo find 9 set the derivative to 0:NlogP（*T&） = 0n=lAnd solve for 0§5・1.1 Maximum Likelihood Estimation=0i二(坯一爲尸N— J ■“ I ” l—・■・2台能2&2L1,ML1 N =山>1 -2.ML =为龙仙-■'i=l他=- ylog处(g) _90W)do2§5・1.1 Maximum Likelihood Estimation Gaussigin P日rmmeter EstimationFollow a similar process to find the parameters for the assumed Gaussian density.If we knew 色E then we could write the probability of samples Mi •・・3 asF *(2 -凶丁刀1(2 -上)(2可炉巨昭——§5・1.1 Maximum Likelihood Estimation We are looking for 色S that maximize this. That is? for6亦戸@1…舸|出£) = 0…・卫N |出= 0First, take log to simplify:/ -JV log ((2TT)^2|S| I") — £若(凹—/x)T S_1(^ — p)£-低一上)}=0 to maximize§5・1.1 Maximum Likelihood EstimationSimilarly for the Govariance matrix…Consider 0 — X-1 for convenience.N [ N十不log\0\ --工;色-兰尸巩弐-/£）7 X舊｛—N如（㈣"）=_ 吉_邑）（爲-进§5・1.1 Maximum Likelihood EstimationBut 9-1 = S and E r = S、 1 N・'・£ = —〉= £）（蚤一£）『=S° i=lwhich is the sample covariance matrix!Note that this form is biased.§5・1.1 Maximum Likelihood Estimation the binomial distribution: 迎型弟c Fnisclassified_We now have th© maximum likelihood values for th© pdf parameters. Th©s© values maximiz© th© probability of the samples observed in the training set.The estimated class 'a priori ,probabilitiesPW)= ； &气 1-矿"where£(8) = logp (冏 9) = log+ 衣1鹉& + (n — A) log(l — 0)dor=7 = 00(Ti — fc)The estimated mean and covarianc$ matrices for a normal distribution，i "S A/L =壬"（鱼 _ _ A）ri=lAre these formulations biased?Definition: An estimate is unbiased if its expected value is its true value.Is the maximum likelihood timate of the mean biased?So the ML mean is unbiased.What is the expected value of the ML estimate of the covariance matrix?, 「1 N I= E —- -. i=l ■1 N=亓[（各_国（各_ ^）T]i=L1 N=jv 匸E [（色—上）—@ —凶）（色—上）—（A - f0）r]一1=1=〒£ E ［（（鱼一£）一（总一£））（（鱼一一（M - M））r］2 i=l1 N=［（2 一毋2 ~E）T _ （弐一£）@_£）丁 -位一£）（弐_£）丁 + （A-M）（A - M）T］i=lHowever, since=［（£—£）（弐—凶了—（g —£）址一色）厂—（A-M）（A-Z£）T + （g—£）（也一色厂］* 2— 1i N- M）（鱼-兰）T - @ - A£）（A - £）订i=l=工一£［@一色）@一色円So the expected value of the ML covariance matrix is the actual covarianee matrix minus a small amount. It is biased.■I " 1 "U 口弐-叭口鱼-兰)Z=^L 1]N N=E E 一兰)％ 一i=L j = l ■ N - £)(蛍-色卩■=1The variance of the sample mean is the variance divided by thenumber of samples.The ML covariance matrix is slightly less than the actual covariance matrix, but becomes a better estimate for large 『values of N.E*[(M - M)(^-A£)r ] = E samples areindependentIn the univariate case, this is equivalent to saying:var(x.i) = a 2人1E\E ML]= E-^EAn unbiased estimate of the covariance matrix is then:亠jy ] f、乩=_ 坐）（鸟-型）丁1 1i=lN》\ and the amount of bias is negligible.Suppose that N samples are independently drawn from a Nonnal distribution with known mean but un-known variance^ .Example 5J:农减仪「Mm ； • •心厂整瘵;专議咚 V 療郭ij'S 打r 綽 齐 P 但内二-^尹扛宁『• " A v • 9 ♦了 » 1f 比熔浮維拐;话※‘腐r 二匚与九，辎幕宅玄L 够｛辛竜衍注工..总;：圧知• ^ 「 ： ^ . ; ■. •.(a) Derive the Maximum Likelihood estirnate for the vmance^(a) The maximum likelihood estimator is derived asi N石耳生一疔_N = 0■* * • *r •.•-•. - ** R v ・** #・ 1 '* * 1i N 瓦平F.<；Asct<,>: •：： •: -，/?呪©) ~dT •‘农知礫 N E T=1N-£ i=l@2 Since the expected value of thc ：cstimate is equal to the true variance, we have art unbiased estimate.(b) To check for unbiasediiess, we compute the expectation of the estimate:吕；・：D 匚E［靜］=E首主任i-“尸-A 1 = 11 V歹若Eg诃；N§ 54.3 Bayes Estimation (Bayes Learning)With ML estimation, we viewed the parameters as fixed values but unknown. Using the training samples, we found the values that maximize the likelihood of obtaining those observed samples.In Bayesian estimation, we try to infer the probabilistic distribution of the parameters from an a priori ©uess” of the distribution and the training samples.Notes for the following pages:・ Each class is approached separately. So the densities need to be calculated for each class.-Samples are assumed to be independent of each other.§5・1・3 Bayes EstimationGiven an assumed form for the p.d.f. of x: 巩圉0)with some parameter (eg. mean): 9and assumed a priori distribution: P (&)(an initial guess that reflects our knowledge and our uncertainty about the para meters)Then Bayes theorem says:The bottom term is a normalizing factor that is in dependent of theta. The drawing of each sample is independent, and so:N卩(0|{%}) =a-卩(0|{監})= 卩({%}冏P W)i=lExample: 1-D Gaussian with Known VarianceConsider the case where the class mean is the only unknown parameter. Assume the distribution is Gaussian.p(a?|0) = N(9、Q2)We have some prior knowledge of the mean - a guess that its mean and variang are:P(0) = JV(p.0,crg)1 _ i / £r±o \2=——一e 珂％ /V27T(7OUsing the prior knowledge, find the a posterior density using the information from the gathered samples.Np(e\{xi}) = a 匸讥9)p(&)N戸(9|{^}) = a[Ji=lThose factors that do not depend on theta have been absorbed into the constants.1. _ -expV'S TTCT§5・1・3 Bayes EstimationBecause the form is an exponential function of a quadratic, the distribution is a normal density! The factors can be rewritten to fit the following form:卫⑹{临})= J- ^.p7 2^(7 N§5.1.3 Bayes EstimationThis yields:INI鬲=庐+龙4N N U Q—= —m H ----------- 寸(m is the sample mean) cr 务Solving:Naim十AN - Ng + 品_2 "鼬2N N代十卢Thus the mean of the parameter theta after N samples is a weighted average of the sample mean and initial estimate of the mean.The variance of the parameter after N samples is affected by the variance of the class, the initial estimate of the parameter variance, and the number of samples.limNcr^m + <T2WO 側=5代花-lim 喝=0N―KOOWhat happens as N gets very large?-20So Bayes estimation allows learning, allowing for initial estimates and then successive modifications to this as samples are gathered and coded.Some extremes:-if parameter variance is 0, the prior certainty is so strong that the prior estimate of the mean will always be used for the conditioneci mean: O Q=QN(J Q7H+缈=N代+辞-if parameter varianee is much larger than the class variance, then the sample mean will be used for the conditioned mean.The final step is to use the information about the mean （the a posterior density） tofind the 'dasAconditionaP density.P（时仙｝） = [ P（邮）P（圳也｝）曲（proof skipped）=A r（Av?^2 + 喲Compare with: p（z|0）="（伏卢）The conditional mean is treated as the real mean, and the known variance is increased to account for the uncertainty of the memAs the number of samples is increased, the distribution of the classconditional density approaches the true distribution.§ 5.2 Non-Parametric EstimationIn parameter estimation, we assumed a form for the distribution and estimated the parameters, either as specific values (ML) or distributions (Bayes5). However if we do not know the specific form of the pdf, then we need a different approach.Density estimation is a non-parametric technique that uses variations of histogram approximation.Simplest case is partitioning the feature space into 'bins'.r\§ 5.2.1 Histogram Estimation>1P(x) is a discrete approximation of p(x)• Count a number of times that x lands in the /-th binH ⑴二N7=1• NormalizeAo =严§ 5.2.1 Histogram Estimation How many bins?J“ M =3 0（兀）心尸（兀）册二20as0 "Oversmoothing''恥）、广吊）^ = 50（兀）0501.Qg/ P（x）IID 才9 —-b 6 «<4Overtittmg,9Good:•Once it is constructed, the data can be discarded •Quick and intuitiveBad:•Very sensitive to number of bins, M •Estimated density is not smoothIK•Poor generalization in higher dimensions •Imagine we build a histogram of a 1-d feature (say, Hue)•10 bins•1 bin = 10% of the input space•need at least 10 points to populate every bin•We add another feature (say?Saturation')•10 bins again•1 bin = 1 % of the input space•we need at least 100 points to populate every bin •We add another feature (say, Value)•10 bins again•1 bin = 0,1% of the input space•we need at least 1000 points to populate every binN = b“ - number of points grows exponentiallyBy definintion:P(x e R) = P = p(x 'RIf we have A 7i.i.d .points drawn form p(x):B(N, P) is a binomial distribution of kN\ = B(N.P)Num. of unique splits K vs. (N-K) Prob that k of particular x-es are in RPiob that therest are notMean and variance of 尸);Mean: " = E[k] = NP P = E[k / N]Variance: (T2 = E[(k— /J.)2] = NP(l — P)nE (k/N-P)2= P(l-P)/NThat is:•E\k/N] is a good estimate of P•P is distributed around this estimate with vanishing varianceSo:P^k/NSo:P^k/NOn the other hand, under mild assumptions:P = 二 p(x )t■ R…which leads to: kNVVolume of R(not pd))Now, given N data points — how do we really estimate 〃(x)?K-Nearest Neighbors (KNN)Kernel methodsWe choose Fby specifying a hypercube with a side hiMathematically:|<l/2J Jotherwisekernel function:^(y)>0, Vy and§522 Parzen Window Estimation Then-a hypercube with side h centered at x1] H can help count the points in a volume V around any x:。

高三英语统计学分析单选题60题及答案1.The average score of a class is calculated by adding all the scores and dividing by the number of students. This is an example of _____.A.meanB.medianC.modeD.range答案：A。

本题考查统计学基本概念。

A 选项mean（平均数）是通过将所有数据相加再除以数据个数得到的，符合题干描述。

B 选项median（（中位数）是将数据从小到大排列后位于中间位置的数。

C 选项mode（众数）是数据中出现次数最多的数。

D 选项range（极差）是数据中的最大值与最小值之差。

2.In a set of data, if there is a value that occurs most frequently, it is called the _____.A.meanB.medianC.modeD.range答案：C。

A 选项mean 是平均数。

B 选项median 是中位数。

C 选项mode 众数是出现次数最多的值，符合题意。

D 选项range 是极差。

3.The middle value in a sorted list of data is called the _____.A.meanB.medianC.modeD.range答案：B。

A 选项mean 是平均数。

B 选项median 中位数是排序后位于中间的数，符合题干描述。

C 选项mode 是众数。

D 选项range 是极差。

4.The difference between the highest and lowest values in a set of data is known as the _____.A.meanB.medianC.modeD.range答案：D。