Functional magnetic resonance imaging (fMRI), which allows researchers to observe neural activity in the human brain noninvasively, has revolutionized the scientific study of the mind. An fMRI experiment produces massive amounts of highly complex data; researchers face significant challenges in analyzing the data they collect. This book offers an overview of the most widely used statistical methods of analyzing fMRI data. Every step is covered, from preprocessing to advanced methods for assessing functional connectivity. The goal is not to describe which buttons to push in the popular software packages but to help readers understand the basic underlying logic, the assumptions, the strengths and weaknesses, and the appropriateness of each method.

The second edition of Statistical Analysis of fMRI Data bears little resemblance to the first edition. There are six new chapters and every chapter from the first edition was updated and significantly revised. The new chapters cover experimental design (Chapter 4), functional connectivity analysis via the methods of psychophysiological interactions and beta-series regression (Chapter 9), decoding via multi-voxel pattern analysis (Chapter 14), encoding models (Chapter 15), dynamic causal modeling (Chapter 16), and representational similarity analysis (Chapter 17). There is also a new appendix that describes how to build a design matrix for group analysis via effect coding (Appendix C). In addition, I made many significant revisions to the other chapters – far too many to list here. A few of the more noteworthy were to include descriptions and discussions of some newly discovered problems related to head movements (Chapter 5), the multivariate GLM (Chapter 6), the extremely high false-positive rates that can occur with the use of cluster-based methods for correcting for multiple comparisons (Chapter 7), and I added a new section on meta-analysis (Chapter 8). Another major change was to move all complex derivations to the end of the relevant chapter in an effort to improve readability.

The necessary mathematics is explained at a conceptual level, but in enough detail to allow mathematically sophisticated readers to gain more than a purely conceptual understanding. The book also includes short examples of Matlab code that implement many of the methods described; and appendices that offer an introduction to basic Matlab matrix algebra commands (as well as a tutorial on matrix algebra), an introduction to multivariate probability distributions, and a tutorial on how to build a design matrix for group analyses.

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Endorsements:

"Understanding the complexities associated with the generation of brain function images is essential, but this information is often difficult to obtain. This lovely new book by Ashby is a major step in meeting that need. I recommend it with enthusiasm to new initiates to imaging as well as seasoned veterans."

-Marcus Raichle, Professor of Radiology, Neurology, Neurobiology, and Biomedical Engineering at Washington University in St Louis

"This book covers all major fMRI analyses with a level of mathematical depth that is appropriate for cognitive and brain scientists with some background in statistics. The author has the rare ability of explaining complex issues using intuitive and engaging prose. The perfect balance between conceptual intelligibility and mathematical rigor makes this an ideal textbook for undergraduate and graduate courses."

-Roberto Cabeza, Professor of Psychology and Neuroscience, Duke University

Download all Matlab Programs

Chapter 3: Modeling the BOLD Response

Box 3.1: Create and plot an hrf

Box 3.2: Convolve an hrf with a boxcar function to create a predicted BOLD response

Box 3.3: Generate BOLD predictions from the Volterra model

Chapter 5: Preprocessing

Box 5.1: Three methods for interpolatiing a difference-of-gammas hrf

Box 5.2: Coregistration using histogram bins

Box 5.3: The matched filter theorem

Box 5.4: High-pass temporal filtering

Chapter 6: The General Linear Model

Box 6.1: Generate a predicted BOLD vector for GLM analysis

Box 6.2: Present a design matrix visually

Box 6.3: Apply the correlation-based GLM to data

Chapter 7: The Multiple Comparisons Problem

Box 7.1: Implementing false discovery rate

Chapter 8: Group Analysis

Box 8.1: Fixed effects and random effects analysis of group data

Box 8.2: Compute the power of the t-test in which the null hypothesis is that there is no difference in activation between task and rest blocks and the alternative hypothesis is that the difference between task and rest is K% signal change

Chapter 10: Granger Causality

Box 10.1: Create and fit autoregressive models of orders 1, 2, and 3

Box 10.2: Compute Granger causality Fx→y

Box 10.3: Compute conditional Granger causality Fi→2|3

Chapter 11: Coherence Analysis

Box 11.1: Compute and plot an autocorrelation function and a cross-correlation function

Box 11.2: Compute the power spectrum of a BOLD response

Box 11.3: Compute coherence between two BOLD responses

Box 11.4: Compute partial coherence between two BOLD responses without and with extra influence between them

Chapter 16: Dynamic Causal Modeling

Box 16.1: Create linear and bilinear models of the figure 16.3 network, then generate predicted neural activations and BOLD response for each region in the model