Linear Models in Medical Imaging. John Kornak MI square February 22, 2011
|
|
- Aron Kelly
- 5 years ago
- Views:
Transcription
1 Linear Models in Medical Imaging John Kornak MI square February 22, 2011
2 Acknowledgement / Disclaimer Many of the slides in this lecture have been adapted from slides available in talks available on the SPM web site.
3 Overview Motivation Linear model formulation Region of interest analyses Pixel/voxel based analyses Multiple comparisons for images Bayesian image analysis methods
4 Motivation Imaging data statistical methods to look for regional effects Tissue differences between groups or over time VBM, TBM (voxel/tensor-based morphometry) PET (positron emmission tomography), fmri (functional MRI) determine activation in the brain due to thought, stimulus or task Diffusion (DWI, DTI, tractography), Bone mineral density etc. etc.
5 FMRI Data: Set of Volumes (over time) or Set of Time-Series (over space) Serial Snapshots of Volunteers brain Time Time Active Passive Baseline
6 Software etc. SPM PET, fmri, VBM and TBM, EEG/MEG ( needs Matlab) FSL fmri primarily + DTI ( R AnalyzeFMRI package + linear models in general ( and then go to your nearest CRAN mirror) Also, check Venables and Ripley Splus book + many R books (see R web site) + online tutorials
7 Challenges Generating suitable (statistical) imaging models Dealing with highly multivariate responses (curse of dimensionality) Defining imaging hypotheses Creating computationally efficient analysis procedures
8 Aims of Statistical Modeling Summarize data Estimation: point and interval estimates Inference: hypotheses / relationships Prediction
9 Aims of Statistical Modeling Summarize data Estimation: point and interval estimates Inference: hypotheses / relationships Prediction
10 Statistical Modeling Strategy Propose a model for the data Fit the model Assess the model s adequacy Fit other plausible models Compare all fitted models Interpret the best model
11 Statistical Models: Definitions Univariate response variable y i (for exp. unit i) Covariates (x i1, x i2,..., x ik ) = (variables of interest and nuisance variables) x i T Data is: { y i,x T i ;i = 1,...,n}, n experimental units Continuous covariates: e.g. age, blood pressure etc., (random or controlled) Factors: e.g. diagnosis, gender, drinking level (low, medium, high) etc.
12 The (General) Linear Model A simple linear model might take the form: e.g. y i =! 1 + x i2! 2 + x i3! x im! m + " i y =! + x! + x! x! + " i mean i, age age i, gender gender i, diagnosis diagnosis i! " = 2 i ~ N(0, ), i. i. d. i 1,..., n i.i.d. = independently and identically distributed
13 The (General) Linear Model For univariate data: y i = x i T! + " i, i = 1,...,n! = (! 1,...,! m ) T or in matrix notation y = X T! + " is a set of unknown parameters This can be extended to a multivariate response Y = X T B + E
14 Ex. Hippocampal Volume HCV ~ Age + Diagnosis (Wilkinson notation) Diagnosis can be normal control (NC) or Alzheimer s disease (AD)
15 Ex. Hippocampal Volume HCV ~ Age + Diagnosis + Age*Diagnosis (Wilkinson notation) Diagnosis can be normal control (NC) or Alzheimer s disease (AD)
16 Structural T1 weighted MRI s Hippocampal volumes manually traced Volume measure = response for each subject Disease status encoded 1 for AD and 0 for NC (the term) x diag.
17 y i =! 1 + x i,age! age + x i,diag.! diag. + x i.age x i,diag.! inter + " i HCV Case 1! = 0,! = 0,! = 0 age diag. inter age
18 y i =! 1 + x i,age! age + x i,diag.! diag. + x i.age x i,diag.! inter + " i HCV Case 2! " 0,! = 0,! = 0 age diag. inter age
19 y =! + x! + x! + x x! + " i 0 i, age age i, diag. diag. i. age i, diag. inter i HCV Case 3! " 0,! " 0,! = 0 age diag. inter NC AD age
20 y =! + x! + x! + x x! + " i 0 i, age age i, diag. diag. i. age i, diag. inter i Case 4! " 0,! " 0,! " 0 age diag. inter HCV NC AD age
21 y i =! 1 + x i,age! age + x i,diag.! diag. + x i.age x i,diag.! inter + " i Case 4! " 0,! " 0,! " 0 age diag. inter HCV NC AD age
22 Linear models can be more general - only needs to be linear in the parameters:! We can have: y = x! + x 2! + exp(x )! + x " x! + # i age 1 age 2 height 3 age height 4 i i = 1,...,n
23 E( ˆ!) =! V ( ˆ!) = # 2 (X T X) "1 Estimation Minimize squared error (Least Squares Error) = Maximum Likelihood Estimation for linear model ˆ! = (X T X) "1 X T y 2 Estimate! by or divide by n-1 sum of squares error ˆ# 2 = for unbiased n estimate
24 Inference Model Comparison Take linear model y = X T! + " And add constraint A! = c this defines a new model that is a simplification of the previous one
25 Inference Model Comparison E.g., cf. model y i =! 1 +! 2 x i1 +! 3 x i2 + " i to simplification with! 3 = 0 " % i.e. y i =! 1 +! 2 x i + " i! 1 $ (0,0,1) $ $ #! 2! 3 ' ' ' & = 0 i.e. A! = c
26 What about &?! 2 = 0! 3 = 0 A! = c " # % % $ & ( ( ' # % % % $! 1! 2! 3 & ( ( ( ' = # % $ 0 0 & ( '
27 And what about?! 2 =! 3 # &! 1 ( ) A! = c " % % % $! 2! 3 ( ( ( ' = 0 Are 2 different conditions equivalent? E.g. is the activation effect: reading a word vs imagining the object equal?
28 Definition: Linear model nested in another if 1 st model can be obtained by linear constraint on the 2 nd Nesting tree: age + gender age gender null
29 F-test for General Linear Hypothesis ( ) y = X T! + " "! N n 0,# 2 I n Consider H 0 : A! = c This is the General Linear Hypothesis
30 Under H 0, i.e., A! = c F = (Dev nested! Dev larger ) / ( p larger! p nested ) (Dev larger ) / (n! p larger )! F plarger! p nested,n! p larger p denotes the number of model parameters n denotes the number of data points Dev = Deviance = sum of squares of residuals Tests ratio of variances
31 FMRI Data: Set of Volumes (over time) or Set of Time-Series (over space) Serial Snapshots of Volunteers brain Time Time Active Passive Baseline
32 image data kernel design matrix parameter estimates realignment & motion correction smoothing Linear Model model fitting statistic image Thresholding & Random Field Theory normalisation anatomical reference Statistical Parametric Map (test statistics) Corrected thresholds & p-values
33 Estimation The estimation entails finding the parameter values such that the linear combination best fits the data Active Passive Baseline
34 Parameter Estimates Same model for all voxels Different parameters for each voxel beta_0001.img Time-series... " 0.83% ˆ! = $ ' $ 0.16 ' # $ 2.98& ' " 0.03% $ ' ˆ! = $ 0.06 ' # $ 2.04 &' beta_0002.img... ˆ! = " 0.68% $ ' $ 0.82 ' # $ 2.17& ' beta_0003.img
35 y X T β SPM View "! 1 % $ ' $! 2 ' $! ' # 3 & Note: We trust: Long series with large effects and small error
36 Spatial Modeling
37 Spatial Hypotheses Question - how do we extend from standard univariate hypotheses to answering spatially motivated questions? Not easy - curse of dimensionality (millions of voxels) in 1D it makes sense to infer A is less than B, but what is the equivalent in 2D?
38 Spatial Testing Solutions Summarize the image into one dimensional quantities for testing (e.g. region of interest analysis) Consider the overall test as a combination of individual voxel tests (voxel based analysis) Perform shape/object analysis on objects defined via landmarks Build Bayesian image analysis models
39 Spatial Testing Solutions Summarize the image into one dimensional quantities for testing (e.g. region of interest analysis) Consider the overall test as a combination of individual voxel tests (voxel based analysis) Perform shape/object analysis on objects defined via landmarks Build Bayesian image analysis models
40 Voxel based analysis Each voxel obtains a test statistic from the linear model, e.g. t or F Forms statistical maps of the statistics
41 image data kernel design matrix parameter estimates realignment & motion correction smoothing Linear Model model fitting statistic image Thresholding & Random Field Theory normalisation anatomical reference Statistical Parametric Map (test statistics) Corrected thresholds & p-values
42 Hypothesis Testing Null Hypothesis H 0 Test statistic T t observed realization of T α-level Acceptable false positive risk Level α = Pr( T>u α H 0 ) Threshold u α controls false positive risk at level α u α Null Distribution of T α
43 Multiple Comparisons Problem Which of 100,000 voxels are significant? α =0.05 5,000 false positive voxels
44 Assessing Statistic Images Where s the signal or change? High Threshold Med. Threshold Low Threshold t > 5.5 t > 3.5 t > 0.5 Good Specificity Poor Power (risk of false negatives) Poor Specificity (risk of false positives) Good Power How can we determine a sensible threshold level?
45 Multiple Comparison Solutions: Measuring False Positives Familywise Error Rate (FWER) Familywise Error Existence of one or more false positives False Discovery Rate (FDR) FDR = E(V/R) R voxels declared active, V falsely so Realized false discovery rate: V/R
46 Bonferroni Correction (v = voxel- FWE, α, for N independent voxels is α = Nv wise error rate) To control FWE set v = α / N Independent Voxels Spatially Correlated Voxels Bonferroni is too conservative for brain images
47 FWER MCP Solutions: Random Field Theory Euler Characteristic χ u Topological Measure No holes Never more than 1 blob #blobs - #holes At high thresholds, just counts blobs Random Field FWER = Pr(Max voxel u H o ) = Pr(One or more blobs H o ) Pr(χ u 1 H o ) E(χ u H o ) Threshold See description at Suprathreshold Sets
48 Random Field Theory Limitations Multivariate normality (Gaussianity) Virtually impossible to check Sufficient smoothness FWHM smoothness 3-4 voxel size Smoothness estimation Estimate is biased when images not sufficiently smooth Several layers of approximations Lattice Image Data Continuous Random Field
49 Multiple Comparisons Solutions: Measuring False Positives Familywise Error Rate (FWER) Familywise Error Existence of one or more false positives FWER is probability of familywise error False Discovery Rate (FDR) FDR = E(V/R) R voxels declared active, V falsely so Realized false discovery rate: V/R
50 False Discovery Rate For any threshold, all voxels can be crossclassified: Null True Null False Accept Null Reject Null V 0A V 0R V 1A V 1R N A N R Realized FDR rfdr = V 0R /(V 1R +V 0R ) = V 0R /N R If N R = 0, rfdr = 0 But only can observe N R, don t know V 1R & V 0R We control the expected rfdr FDR = E(rFDR)
51 False Discovery Rate Illustration: Noise Signal Signal+Noise
52 Control of Per Comparison Rate at 10% 11.3% 11.3% 12.5% 10.8% 11.5% 10.0% 10.7% 11.2% 10.2% 9.5% Control of Familywise Error Rate at 10% Occurrence of Familywise Error FWE Control of False Discovery Rate at 10% 6.7% 10.4% 14.9% 9.3% 16.2% 13.8% 14.0% 10.5% 12.2% 8.7% Percentage of Observed Above Threshold Pixels that are False Positives
53 Benjamini & Hochberg Procedure Select desired limit q on FDR Order p-values, p (1) p (2)... p (V) Let r be largest i such that p (i) i/v q/c(v) Reject all hypotheses corresponding to p (1),..., p (r) p NB, no spatial consideration Journal of the Royal Statistical Society Series B (1995) 57: i/v p (i) i/v q/c(v)
54 Also, Non-Parametric Testing If H 0 is true then time order irrelevant (if noise really iid) Therefore permute the timepoints and obtain test statistics If true test statistic is extreme compared to others then reject H 0
55 Types of Spatial Inference Individual voxel level Cluster level Set level Bayesian model based
56 Voxel-level Inference Retain voxels above α-level threshold u α Gives best spatial specificity H 0 at a single voxel can be rejected u α space Significant Voxels No significant Voxels
57 Cluster-level Inference Two step-process Define clusters by arbitrary threshold u clus Retain clusters larger than α-level threshold k α u space Cluster not significant k α k α Cluster significant
58 Cluster-level Inference Typically better sensitivity Worse spatial specificity The null hyp. of entire cluster is rejected Only means that one or more of voxels in cluster active u space Cluster not significant k α k α Cluster significant
59 Set-level Inference Count number of blobs c Minimum blob size k Worst spatial specificity Only can reject global null hypothesis u k k space Here c = 1; only 1 cluster larger than k
60 Review: Levels of inference & power
61 A flexible Bayesian Approach Model the form of activity Provides an adaptive thresholding approach space Active voxels
62 Bayesian Model y = zx +! y = data, parameter estimates of statistics z = binary activation map modeled as a MRF x = activation level field modeled as a MRF = residual error! MRF = Markov Random Field (similar random field but defined on a lattice)
63 x Model Illustration zx +! z = 0 z = 1 z = 0
64 Model Illustration x zx fit z = 0 z = 1 z = 0
65 y x z zx +! =
66 Other Topics and Omissions Hemodynamic response function Multiple subjects (random and mixed effects models) PCA, ICA Multivariate analysis with variogram modeling Space-time modeling
Linear Models in Medical Imaging. John Kornak MI square February 23, 2010
Linear Models in Medical Imaging John Kornak MI square February 23, 2010 Acknowledgement / Disclaimer Many of the slides in this lecture have been adapted from slides available in talks available on the
More informationLinear Models in Medical Imaging. John Kornak MI square February 19, 2013
Linear Models in Medical Imaging John Kornak MI square February 19, 2013 Acknowledgement / Disclaimer Many of the slides in this lecture have been adapted from slides available in talks available on the
More informationLinear Models in Medical Imaging. John Kornak MI square February 21, 2012
Linear Models in Medical Imaging John Kornak MI square February 21, 2012 Acknowledgement / Disclaimer Many of the slides in this lecture have been adapted from slides available in talks available on the
More informationIntroductory Concepts for Voxel-Based Statistical Analysis
Introductory Concepts for Voxel-Based Statistical Analysis John Kornak University of California, San Francisco Department of Radiology and Biomedical Imaging Department of Epidemiology and Biostatistics
More informationNew and best-practice approaches to thresholding
New and best-practice approaches to thresholding Thomas Nichols, Ph.D. Department of Statistics & Warwick Manufacturing Group University of Warwick FIL SPM Course 17 May, 2012 1 Overview Why threshold?
More informationMultiple Testing and Thresholding
Multiple Testing and Thresholding UCLA Advanced NeuroImaging Summer School, 2007 Thanks for the slides Tom Nichols! Overview Multiple Testing Problem Which of my 100,000 voxels are active? Two methods
More informationMultiple Testing and Thresholding
Multiple Testing and Thresholding NITP, 2009 Thanks for the slides Tom Nichols! Overview Multiple Testing Problem Which of my 100,000 voxels are active? Two methods for controlling false positives Familywise
More informationMultiple comparisons problem and solutions
Multiple comparisons problem and solutions James M. Kilner http://sites.google.com/site/kilnerlab/home What is the multiple comparisons problem How can it be avoided Ways to correct for the multiple comparisons
More informationMultiple Testing and Thresholding
Multiple Testing and Thresholding NITP, 2010 Thanks for the slides Tom Nichols! Overview Multiple Testing Problem Which of my 100,000 voxels are active? Two methods for controlling false positives Familywise
More informationCorrection for multiple comparisons. Cyril Pernet, PhD SBIRC/SINAPSE University of Edinburgh
Correction for multiple comparisons Cyril Pernet, PhD SBIRC/SINAPSE University of Edinburgh Overview Multiple comparisons correction procedures Levels of inferences (set, cluster, voxel) Circularity issues
More informationExtending the GLM. Outline. Mixed effects motivation Evaluating mixed effects methods Three methods. Conclusions. Overview
Extending the GLM So far, we have considered the GLM for one run in one subject The same logic can be applied to multiple runs and multiple subjects GLM Stats For any given region, we can evaluate the
More informationMedical Image Analysis
Medical Image Analysis Instructor: Moo K. Chung mchung@stat.wisc.edu Lecture 10. Multiple Comparisons March 06, 2007 This lecture will show you how to construct P-value maps fmri Multiple Comparisons 4-Dimensional
More informationControlling for multiple comparisons in imaging analysis. Wednesday, Lecture 2 Jeanette Mumford University of Wisconsin - Madison
Controlling for multiple comparisons in imaging analysis Wednesday, Lecture 2 Jeanette Mumford University of Wisconsin - Madison Motivation Run 100 hypothesis tests on null data using p
More informationCHAPTER 2. Morphometry on rodent brains. A.E.H. Scheenstra J. Dijkstra L. van der Weerd
CHAPTER 2 Morphometry on rodent brains A.E.H. Scheenstra J. Dijkstra L. van der Weerd This chapter was adapted from: Volumetry and other quantitative measurements to assess the rodent brain, In vivo NMR
More informationControlling for mul2ple comparisons in imaging analysis. Where we re going. Where we re going 8/15/16
Controlling for mul2ple comparisons in imaging analysis Wednesday, Lecture 2 Jeane?e Mumford University of Wisconsin - Madison Where we re going Review of hypothesis tes2ng introduce mul2ple tes2ng problem
More informationControlling for mul-ple comparisons in imaging analysis. Wednesday, Lecture 2 Jeane:e Mumford University of Wisconsin - Madison
Controlling for mul-ple comparisons in imaging analysis Wednesday, Lecture 2 Jeane:e Mumford University of Wisconsin - Madison Where we re going Review of hypothesis tes-ng introduce mul-ple tes-ng problem
More informationIntroduction to Neuroimaging Janaina Mourao-Miranda
Introduction to Neuroimaging Janaina Mourao-Miranda Neuroimaging techniques have changed the way neuroscientists address questions about functional anatomy, especially in relation to behavior and clinical
More informationContents. comparison. Multiple comparison problem. Recap & Introduction Inference & multiple. «Take home» message. DISCOS SPM course, CRC, Liège, 2009
DISCOS SPM course, CRC, Liège, 2009 Contents Multiple comparison problem Recap & Introduction Inference & multiple comparison «Take home» message C. Phillips, Centre de Recherches du Cyclotron, ULg, Belgium
More information7/15/2016 ARE YOUR ANALYSES TOO WHY IS YOUR ANALYSIS PARAMETRIC? PARAMETRIC? That s not Normal!
ARE YOUR ANALYSES TOO PARAMETRIC? That s not Normal! Martin M Monti http://montilab.psych.ucla.edu WHY IS YOUR ANALYSIS PARAMETRIC? i. Optimal power (defined as the probability to detect a real difference)
More informationNeuroimaging and mathematical modelling Lesson 2: Voxel Based Morphometry
Neuroimaging and mathematical modelling Lesson 2: Voxel Based Morphometry Nivedita Agarwal, MD Nivedita.agarwal@apss.tn.it Nivedita.agarwal@unitn.it Volume and surface morphometry Brain volume White matter
More informationZurich SPM Course Voxel-Based Morphometry. Ged Ridgway (Oxford & UCL) With thanks to John Ashburner and the FIL Methods Group
Zurich SPM Course 2015 Voxel-Based Morphometry Ged Ridgway (Oxford & UCL) With thanks to John Ashburner and the FIL Methods Group Examples applications of VBM Many scientifically or clinically interesting
More informationComputational Neuroanatomy
Computational Neuroanatomy John Ashburner john@fil.ion.ucl.ac.uk Smoothing Motion Correction Between Modality Co-registration Spatial Normalisation Segmentation Morphometry Overview fmri time-series kernel
More informationStatistical Methods in functional MRI. False Discovery Rate. Issues with FWER. Lecture 7.2: Multiple Comparisons ( ) 04/25/13
Statistical Methods in functional MRI Lecture 7.2: Multiple Comparisons 04/25/13 Martin Lindquist Department of iostatistics Johns Hopkins University Issues with FWER Methods that control the FWER (onferroni,
More informationAnalysis of Functional MRI Timeseries Data Using Signal Processing Techniques
Analysis of Functional MRI Timeseries Data Using Signal Processing Techniques Sea Chen Department of Biomedical Engineering Advisors: Dr. Charles A. Bouman and Dr. Mark J. Lowe S. Chen Final Exam October
More informationBasic Introduction to Data Analysis. Block Design Demonstration. Robert Savoy
Basic Introduction to Data Analysis Block Design Demonstration Robert Savoy Sample Block Design Experiment Demonstration Use of Visual and Motor Task Separability of Responses Combined Visual and Motor
More informationSupplementary methods
Supplementary methods This section provides additional technical details on the sample, the applied imaging and analysis steps and methods. Structural imaging Trained radiographers placed all participants
More informationStatistical Analysis of Neuroimaging Data. Phebe Kemmer BIOS 516 Sept 24, 2015
Statistical Analysis of Neuroimaging Data Phebe Kemmer BIOS 516 Sept 24, 2015 Review from last time Structural Imaging modalities MRI, CAT, DTI (diffusion tensor imaging) Functional Imaging modalities
More information1 Introduction Motivation and Aims Functional Imaging Computational Neuroanatomy... 12
Contents 1 Introduction 10 1.1 Motivation and Aims....... 10 1.1.1 Functional Imaging.... 10 1.1.2 Computational Neuroanatomy... 12 1.2 Overview of Chapters... 14 2 Rigid Body Registration 18 2.1 Introduction.....
More informationAdvances in FDR for fmri -p.1
Advances in FDR for fmri Ruth Heller Department of Statistics, University of Pennsylvania Joint work with: Yoav Benjamini, Nava Rubin, Damian Stanley, Daniel Yekutieli, Yulia Golland, Rafael Malach Advances
More informationFunctional MRI in Clinical Research and Practice Preprocessing
Functional MRI in Clinical Research and Practice Preprocessing fmri Preprocessing Slice timing correction Geometric distortion correction Head motion correction Temporal filtering Intensity normalization
More informationMultiVariate Bayesian (MVB) decoding of brain images
MultiVariate Bayesian (MVB) decoding of brain images Alexa Morcom Edinburgh SPM course 2015 With thanks to J. Daunizeau, K. Brodersen for slides stimulus behaviour encoding of sensorial or cognitive state?
More informationA Non-Parametric Approach
Andrew P. Holmes. Ph.D., 1994. Chapter Six A Non-Parametric Approach In this chapter, a non-parametric approach to assessing functional mapping experiments is presented. A multiple comparisons randomisation
More informationStatistical Methods in functional MRI. Standard Analysis. Data Processing Pipeline. Multiple Comparisons Problem. Multiple Comparisons Problem
Statistical Methods in fnctional MRI Lectre 7: Mltiple Comparisons 04/3/13 Martin Lindqist Department of Biostatistics Johns Hopkins University Data Processing Pipeline Standard Analysis Data Acqisition
More informationBayesian Inference in fmri Will Penny
Bayesian Inference in fmri Will Penny Bayesian Approaches in Neuroscience Karolinska Institutet, Stockholm February 2016 Overview Posterior Probability Maps Hemodynamic Response Functions Population
More informationStatistical inference on images
7 Statistical inference on images The goal of statistical inference is to make decisions based on our data, while accounting for uncertainty due to noise in the data. From a broad perspective, statistical
More informationBasic fmri Design and Analysis. Preprocessing
Basic fmri Design and Analysis Preprocessing fmri Preprocessing Slice timing correction Geometric distortion correction Head motion correction Temporal filtering Intensity normalization Spatial filtering
More informationStatistical Analysis of Metabolomics Data. Xiuxia Du Department of Bioinformatics & Genomics University of North Carolina at Charlotte
Statistical Analysis of Metabolomics Data Xiuxia Du Department of Bioinformatics & Genomics University of North Carolina at Charlotte Outline Introduction Data pre-treatment 1. Normalization 2. Centering,
More informationPower analysis. Wednesday, Lecture 3 Jeanette Mumford University of Wisconsin - Madison
Power analysis Wednesday, Lecture 3 Jeanette Mumford University of Wisconsin - Madison Power Analysis-Why? To answer the question. How many subjects do I need for my study? How many runs per subject should
More informationChapter 6: Linear Model Selection and Regularization
Chapter 6: Linear Model Selection and Regularization As p (the number of predictors) comes close to or exceeds n (the sample size) standard linear regression is faced with problems. The variance of the
More informationSPM8 for Basic and Clinical Investigators. Preprocessing. fmri Preprocessing
SPM8 for Basic and Clinical Investigators Preprocessing fmri Preprocessing Slice timing correction Geometric distortion correction Head motion correction Temporal filtering Intensity normalization Spatial
More informationIntroduction to machine learning, pattern recognition and statistical data modelling Coryn Bailer-Jones
Introduction to machine learning, pattern recognition and statistical data modelling Coryn Bailer-Jones What is machine learning? Data interpretation describing relationship between predictors and responses
More informationMethods for data preprocessing
Methods for data preprocessing John Ashburner Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK. Overview Voxel-Based Morphometry Morphometry in general Volumetrics VBM preprocessing
More informationModelling Neuroimaging Data Using the General Linear Model (GLM Karl) Jesper Andersson KI, Stockholm & BRU, Helsinki
Modelling Neuroimaging Data Using the General Linear Model (GLM Karl) Jesper Andersson KI, Stockholm & BRU, Helsinki No escaping this one fmri time-series Design matrix Parameter Estimates Motion Correction
More informationThe Effect of Correlation and Error Rate Specification on Thresholding Methods in fmri Analysis
The Effect of Correlation and Error Rate Specification on Thresholding Methods in fmri Analysis Brent R. Logan and Daniel B. Rowe, Division of Biostatistics and Department of Biophysics Division of Biostatistics
More informationSnPM is an SPM toolbox developed by Andrew Holmes & Tom Nichols
1 of 14 3/30/2005 9:24 PM SnPM A Worked fmri Example SnPM is an SPM toolbox developed by Andrew Holmes & Tom Nichols This page... introduction example data background design setup computation viewing results
More informationStatistics 202: Data Mining. c Jonathan Taylor. Outliers Based in part on slides from textbook, slides of Susan Holmes.
Outliers Based in part on slides from textbook, slides of Susan Holmes December 2, 2012 1 / 1 Concepts What is an outlier? The set of data points that are considerably different than the remainder of the
More informationPattern Recognition for Neuroimaging Data
Pattern Recognition for Neuroimaging Data Edinburgh, SPM course April 2013 C. Phillips, Cyclotron Research Centre, ULg, Belgium http://www.cyclotron.ulg.ac.be Overview Introduction Univariate & multivariate
More informationPart I. Hierarchical clustering. Hierarchical Clustering. Hierarchical clustering. Produces a set of nested clusters organized as a
Week 9 Based in part on slides from textbook, slides of Susan Holmes Part I December 2, 2012 Hierarchical Clustering 1 / 1 Produces a set of nested clusters organized as a Hierarchical hierarchical clustering
More informationEPI Data Are Acquired Serially. EPI Data Are Acquired Serially 10/23/2011. Functional Connectivity Preprocessing. fmri Preprocessing
Functional Connectivity Preprocessing Geometric distortion Head motion Geometric distortion Head motion EPI Data Are Acquired Serially EPI Data Are Acquired Serially descending 1 EPI Data Are Acquired
More informationNetwork statistics and thresholding
Network statistics and thresholding Andrew Zalesky azalesky@unimelb.edu.au HBM Educational Course June 25, 2017 Network thresholding Unthresholded Moderate thresholding Severe thresholding Strong link
More informationVoxel-Based Morphometry & DARTEL. Ged Ridgway, London With thanks to John Ashburner and the FIL Methods Group
Zurich SPM Course 2012 Voxel-Based Morphometry & DARTEL Ged Ridgway, London With thanks to John Ashburner and the FIL Methods Group Aims of computational neuroanatomy * Many interesting and clinically
More informationFunction-Structure Integration in FreeSurfer
Function-Structure Integration in FreeSurfer Outline Function-Structure Integration Function-Structure Registration in FreeSurfer fmri Analysis Preprocessing First-Level Analysis Higher-Level (Group) Analysis
More informationNeuroimage Processing
Neuroimage Processing Instructor: Moo K. Chung mkchung@wisc.edu Lecture 2-3. General Linear Models (GLM) Voxel-based Morphometry (VBM) September 11, 2009 What is GLM The general linear model (GLM) is a
More informationGraphical Models, Bayesian Method, Sampling, and Variational Inference
Graphical Models, Bayesian Method, Sampling, and Variational Inference With Application in Function MRI Analysis and Other Imaging Problems Wei Liu Scientific Computing and Imaging Institute University
More informationSelected topics on fmri image processing
fmri Symposium, 24 January, 2006, Ghent Selected topics on fmri image processing Jan Sijbers The fmri folks of the Vision Lab UZA Bio-Imaging Lab Vision Lab Univ. Maastricht T.U. Delft 1 Overview generalized
More informationDecoding analyses. Neuroimaging: Pattern Analysis 2017
Decoding analyses Neuroimaging: Pattern Analysis 2017 Scope Conceptual explanation of decoding/machine learning (ML) and related concepts; Not about mathematical basis of ML algorithms! Learning goals
More informationGeneralized additive models I
I Patrick Breheny October 6 Patrick Breheny BST 764: Applied Statistical Modeling 1/18 Introduction Thus far, we have discussed nonparametric regression involving a single covariate In practice, we often
More informationWildfire Chances and Probabilistic Risk Assessment
Wildfire Chances and Probabilistic Risk Assessment D R Brillinger, H K Preisler and H M Naderi Statistics Department University of California Berkeley, CA, 97-386 Pacific Southwest Research Station USDA
More informationDetecting Changes In Non-Isotropic Images
Detecting Changes In Non-Isotropic Images K.J. Worsley 1, M. Andermann 1, T. Koulis 1, D. MacDonald, 2 and A.C. Evans 2 August 4, 1999 1 Department of Mathematics and Statistics, 2 Montreal Neurological
More informationEMPIRICALLY INVESTIGATING THE STATISTICAL VALIDITY OF SPM, FSL AND AFNI FOR SINGLE SUBJECT FMRI ANALYSIS
EMPIRICALLY INVESTIGATING THE STATISTICAL VALIDITY OF SPM, FSL AND AFNI FOR SINGLE SUBJECT FMRI ANALYSIS Anders Eklund a,b,c, Thomas Nichols d, Mats Andersson a,c, Hans Knutsson a,c a Department of Biomedical
More informationPreprocessing II: Between Subjects John Ashburner
Preprocessing II: Between Subjects John Ashburner Pre-processing Overview Statistics or whatever fmri time-series Anatomical MRI Template Smoothed Estimate Spatial Norm Motion Correct Smooth Coregister
More informationBayesian Spatiotemporal Modeling with Hierarchical Spatial Priors for fmri
Bayesian Spatiotemporal Modeling with Hierarchical Spatial Priors for fmri Galin L. Jones 1 School of Statistics University of Minnesota March 2015 1 Joint with Martin Bezener and John Hughes Experiment
More informationRecap: Gaussian (or Normal) Distribution. Recap: Minimizing the Expected Loss. Topics of This Lecture. Recap: Maximum Likelihood Approach
Truth Course Outline Machine Learning Lecture 3 Fundamentals (2 weeks) Bayes Decision Theory Probability Density Estimation Probability Density Estimation II 2.04.205 Discriminative Approaches (5 weeks)
More informationFirst-level fmri modeling
First-level fmri modeling Monday, Lecture 3 Jeanette Mumford University of Wisconsin - Madison What do we need to remember from the last lecture? What is the general structure of a t- statistic? How about
More informationCPSC 340: Machine Learning and Data Mining. Principal Component Analysis Fall 2017
CPSC 340: Machine Learning and Data Mining Principal Component Analysis Fall 2017 Assignment 3: 2 late days to hand in tonight. Admin Assignment 4: Due Friday of next week. Last Time: MAP Estimation MAP
More informationJournal of Articles in Support of The Null Hypothesis
Data Preprocessing Martin M. Monti, PhD UCLA Psychology NITP 2016 Typical (task-based) fmri analysis sequence Image Pre-processing Single Subject Analysis Group Analysis Journal of Articles in Support
More informationNA-MIC National Alliance for Medical Image Computing fmri Data Analysis
NA-MIC fmri Data Analysis Sonia Pujol, Ph.D. Wendy Plesniak, Ph.D. Randy Gollub, M.D., Ph.D. Acknowledgments NIH U54EB005149 Neuroimage Analysis Center NIH P41RR013218 FIRST Biomedical Informatics Research
More informationNorbert Schuff VA Medical Center and UCSF
Norbert Schuff Medical Center and UCSF Norbert.schuff@ucsf.edu Medical Imaging Informatics N.Schuff Course # 170.03 Slide 1/67 Objective Learn the principle segmentation techniques Understand the role
More informationTutorial MICCAI'04. fmri data analysis: state of the art and future challenges. Jean-Baptiste Poline Philippe Ciuciu Alexis Roche
Tutorial MICCAI'04 fmri data analysis: state of the art and future challenges Jean-Baptiste Poline Philippe Ciuciu Alexis Roche CEA/SHFJ, Orsay (France) Goal of this tutorial and plan I. Talk 1: will orientate
More informationFMRI Pre-Processing and Model- Based Statistics
FMRI Pre-Processing and Model- Based Statistics Brief intro to FMRI experiments and analysis FMRI pre-stats image processing Simple Single-Subject Statistics Multi-Level FMRI Analysis Advanced FMRI Analysis
More informationBayesian Methods in Functional Magnetic Resonance Imaging
Bayesian Methods in Functional Magnetic Resonance Imaging Galin L. Jones Kuo-Jung Lee Brian S. Caffo Susan Spear Bassett Abstract: One of the major objectives of functional magnetic resonance imaging studies
More informationSPM8 for Basic and Clinical Investigators. Preprocessing
SPM8 for Basic and Clinical Investigators Preprocessing fmri Preprocessing Slice timing correction Geometric distortion correction Head motion correction Temporal filtering Intensity normalization Spatial
More informationDimension Reduction for Big Data Analysis. Dan Shen. Department of Mathematics & Statistics University of South Florida.
Dimension Reduction for Big Data Analysis Dan Shen Department of Mathematics & Statistics University of South Florida danshen@usf.edu October 24, 2014 1 Outline Multiscale weighted PCA for Image Analysis
More information3 Feature Selection & Feature Extraction
3 Feature Selection & Feature Extraction Overview: 3.1 Introduction 3.2 Feature Extraction 3.3 Feature Selection 3.3.1 Max-Dependency, Max-Relevance, Min-Redundancy 3.3.2 Relevance Filter 3.3.3 Redundancy
More informationCognitive States Detection in fmri Data Analysis using incremental PCA
Department of Computer Engineering Cognitive States Detection in fmri Data Analysis using incremental PCA Hoang Trong Minh Tuan, Yonggwan Won*, Hyung-Jeong Yang International Conference on Computational
More informationCSE 586 Final Programming Project Spring 2011 Due date: Tuesday, May 3
CSE 586 Final Programming Project Spring 2011 Due date: Tuesday, May 3 What I have in mind for our last programming project is to do something with either graphical models or random sampling. A few ideas
More informationCPSC 340: Machine Learning and Data Mining. Principal Component Analysis Fall 2016
CPSC 340: Machine Learning and Data Mining Principal Component Analysis Fall 2016 A2/Midterm: Admin Grades/solutions will be posted after class. Assignment 4: Posted, due November 14. Extra office hours:
More informationfmri Basics: Single Subject Analysis
fmri Basics: Single Subject Analysis This session is intended to give an overview of the basic process of setting up a general linear model for a single subject. This stage of the analysis is also variously
More informationSpatial Regularization of Functional Connectivity Using High-Dimensional Markov Random Fields
Spatial Regularization of Functional Connectivity Using High-Dimensional Markov Random Fields Wei Liu 1, Peihong Zhu 1, Jeffrey S. Anderson 2, Deborah Yurgelun-Todd 3, and P. Thomas Fletcher 1 1 Scientific
More informationBig Data Methods. Chapter 5: Machine learning. Big Data Methods, Chapter 5, Slide 1
Big Data Methods Chapter 5: Machine learning Big Data Methods, Chapter 5, Slide 1 5.1 Introduction to machine learning What is machine learning? Concerned with the study and development of algorithms that
More informationfmri pre-processing Juergen Dukart
fmri pre-processing Juergen Dukart Outline Why do we need pre-processing? fmri pre-processing Slice time correction Realignment Unwarping Coregistration Spatial normalisation Smoothing Overview fmri time-series
More informationAnalysis of fmri data within Brainvisa Example with the Saccades database
Analysis of fmri data within Brainvisa Example with the Saccades database 18/11/2009 Note : All the sentences in italic correspond to informations relative to the specific dataset under study TP participants
More informationStructural Segmentation
Structural Segmentation FAST tissue-type segmentation FIRST sub-cortical structure segmentation FSL-VBM voxelwise grey-matter density analysis SIENA atrophy analysis FAST FMRIB s Automated Segmentation
More informationThe Anatomical Equivalence Class Formulation and its Application to Shape-based Computational Neuroanatomy
The Anatomical Equivalence Class Formulation and its Application to Shape-based Computational Neuroanatomy Sokratis K. Makrogiannis, PhD From post-doctoral research at SBIA lab, Department of Radiology,
More informationQuantitative MRI of the Brain: Investigation of Cerebral Gray and White Matter Diseases
Quantities Measured by MR - Quantitative MRI of the Brain: Investigation of Cerebral Gray and White Matter Diseases Static parameters (influenced by molecular environment): T, T* (transverse relaxation)
More informationEstimating Noise and Dimensionality in BCI Data Sets: Towards Illiteracy Comprehension
Estimating Noise and Dimensionality in BCI Data Sets: Towards Illiteracy Comprehension Claudia Sannelli, Mikio Braun, Michael Tangermann, Klaus-Robert Müller, Machine Learning Laboratory, Dept. Computer
More informationMultivariate Capability Analysis
Multivariate Capability Analysis Summary... 1 Data Input... 3 Analysis Summary... 4 Capability Plot... 5 Capability Indices... 6 Capability Ellipse... 7 Correlation Matrix... 8 Tests for Normality... 8
More informationMultivariate pattern classification
Multivariate pattern classification Thomas Wolbers Space & Ageing Laboratory (www.sal.mvm.ed.ac.uk) Centre for Cognitive and Neural Systems & Centre for Cognitive Ageing and Cognitive Epidemiology Outline
More informationFast or furious? - User analysis of SF Express Inc
CS 229 PROJECT, DEC. 2017 1 Fast or furious? - User analysis of SF Express Inc Gege Wen@gegewen, Yiyuan Zhang@yiyuan12, Kezhen Zhao@zkz I. MOTIVATION The motivation of this project is to predict the likelihood
More informationAn independent component analysis based tool for exploring functional connections in the brain
An independent component analysis based tool for exploring functional connections in the brain S. M. Rolfe a, L. Finney b, R. F. Tungaraza b, J. Guan b, L.G. Shapiro b, J. F. Brinkely b, A. Poliakov c,
More informationMR IMAGE SEGMENTATION
MR IMAGE SEGMENTATION Prepared by : Monil Shah What is Segmentation? Partitioning a region or regions of interest in images such that each region corresponds to one or more anatomic structures Classification
More informationBasic principles of MR image analysis. Basic principles of MR image analysis. Basic principles of MR image analysis
Basic principles of MR image analysis Basic principles of MR image analysis Julien Milles Leiden University Medical Center Terminology of fmri Brain extraction Registration Linear registration Non-linear
More informationThe Optimal Discovery Procedure: A New Approach to Simultaneous Significance Testing
UW Biostatistics Working Paper Series 9-6-2005 The Optimal Discovery Procedure: A New Approach to Simultaneous Significance Testing John D. Storey University of Washington, jstorey@u.washington.edu Suggested
More informationLast time... Coryn Bailer-Jones. check and if appropriate remove outliers, errors etc. linear regression
Machine learning, pattern recognition and statistical data modelling Lecture 3. Linear Methods (part 1) Coryn Bailer-Jones Last time... curse of dimensionality local methods quickly become nonlocal as
More informationClassification. Vladimir Curic. Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University
Classification Vladimir Curic Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Outline An overview on classification Basics of classification How to choose appropriate
More informationStructural Segmentation
Structural Segmentation FAST tissue-type segmentation FIRST sub-cortical structure segmentation FSL-VBM voxelwise grey-matter density analysis SIENA atrophy analysis FAST FMRIB s Automated Segmentation
More informationInstance-based Learning
Instance-based Learning Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University February 19 th, 2007 2005-2007 Carlos Guestrin 1 Why not just use Linear Regression? 2005-2007 Carlos Guestrin
More informationBias in Resampling-Based Thresholding of Statistical Maps in fmri
Bias in Resampling-Based Thresholding of Statistical Maps in fmri Ola Friman and Carl-Fredrik Westin Laboratory of Mathematics in Imaging, Department of Radiology Brigham and Women s Hospital, Harvard
More informationAn Introduction To Automatic Tissue Classification Of Brain MRI. Colm Elliott Mar 2014
An Introduction To Automatic Tissue Classification Of Brain MRI Colm Elliott Mar 2014 Tissue Classification Tissue classification is part of many processing pipelines. We often want to classify each voxel
More informationCluster failure: Why fmri inferences for spatial extent have inflated false positive rates
Supporting Information Appendix Cluster failure: Why fmri inferences for spatial extent have inflated false positive rates Anders Eklund, Thomas Nichols, Hans Knutsson Methods Resting state fmri data Resting
More information