The mental representations of perceptual and cognitive stimuli vary on many dimensions. In addition, because of quantal fluctuations in the stimulus, spontaneous neural activity, and fluctuations in arousal and attentiveness, mental events are characterized by an inherent variability. During the last several years, a number of models and theories have been developed that explicitly assume the appropriate mental representation is both multidimensional and probabilistic. This new approach has the potential to revolutionize the study of perception and cognition in the same way that signal detection theory revolutionized the study of psychophysics. This unique volume is the first to critically survey this important new area of research.

The field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made both in traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the original Handbook, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. The third volume provides up-to-date, foundational chapters on early vision, psychophysics and scaling, multisensory integration, learning and memory, cognitive control, approximate Bayesian computation, and encoding models in neuroimaging.

The mental representations of perceptual and cognitive stimuli vary on many dimensions. In addition, because of quantal fluctuations in the stimulus, spontaneous neural activity, and fluctuations in arousal and attentiveness, mental events are characterized by an inherent variability. During the last several years, a number of models and theories have been developed that explicitly assume the appropriate mental representation is both multidimensional and probabilistic. This new approach has the potential to revolutionize the study of perception and cognition in the same way that signal detection theory revolutionized the study of psychophysics. This unique volume is the first to critically survey this important new area of research.

A guide to all aspects of experimental design and data analysis for fMRI experiments, completely revised and updated for the second edition. 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 for researchers to analyze. This book describes all aspects of experimental design and data analysis for fMRI experiments, covering every step-from preprocessing to advanced methods for assessing functional connectivity-as well as the most popular multivariate approaches. The goal is not to describe which buttons to push in the popular software packages but to help researchers understand the basic underlying logic, the assumptions, the strengths and weaknesses, and the appropriateness of each method. The field of fMRI research has advanced dramatically in recent years, in both methodology and technology, and this second edition has been completely revised and updated. Six new chapters cover experimental design, functional connectivity analysis through the methods of psychophysiological interactions and beta-series regression, decoding using multi-voxel pattern analysis, dynamic causal modeling, and representational similarity analysis. Other chapters offer new material on recently discovered problems related to head movements, the multivariate GLM, meta-analysis, and other topics. All complex derivations now appear at the end of the relevant chapter to improve readability. A new appendix describes how to build a design matrix with effect coding for group analysis. As in the first edition, MATLAB code is provided with which readers can implement many of the methods described.