Bayesian Models of Perception and Action

An accessible introduction to constructing and interpreting Bayesian models of perceptual decision-making and action.

Many forms of perception and action can be mathematically modeled as probabilistic—or Bayesian—inference, a method used to draw conclusions from uncertain evidence. According to these models, the human mind behaves like a capable data scientist or crime scene investigator when dealing with noisy and ambiguous data. This textbook provides an approachable introduction to constructing and reasoning with probabilistic models of perceptual decision-making and action. Featuring extensive examples and illustrations, Bayesian Models of Perception and Action is the first textbook to teach this widely used computational framework to beginners.

• Introduces Bayesian models of perception and action, which are central to cognitive science and neuroscience
• Beginner-friendly pedagogy includes intuitive examples, daily life illustrations, and gradual progression of complex concepts
• Broad appeal for students across psychology, neuroscience, cognitive science, linguistics, and mathematics
• Written by leaders in the field of computational approaches to mind and brain

Acknowledgments xv
The Four Steps of Bayesian Modeling xvii
List of Acronyms xix

Introduction 1
1 Uncertainty and Inference 7
2 Using Bayes' Rule 31
3 Bayesian Inference under Measurement Noise 53
4 The Response Distribution 83
5 Cue Combination and Evidence Accumulation 105
6 Learning as Inference 125
7 Discrimination and Detection 147
8 Binary Classification 169
9 Top-Level Nuisance Variables and Ambiguity 191
10 Same-Different Judgment 205
11 Search 227
12 Inference in a Changing World 245
13 Combining Inference with Utility 257
14 The Neural Likelihood Function 281
15 Bayesian Models in Context 301

Appendices 311
A Notation 313
B Basics of Probability Theory 315
C Model Fitting and Model Comparison 343

Bibliography 361
Index 371Wei Ji Ma is Professor of Neural Science and Psychology at New York University, founder of the Growing up in Science series, and a founding member of the Scientist Action and Advocacy Network. Konrad Paul Kording is Professor of Bioengineering and Neuroscience at the University of Pennsylvania, cofounder of Neuromatch, and codirector of the CIFAR Program in Learning in Machines & Brains. Daniel Goldreich is Associate Professor of Psychology, Neuroscience, and Behaviour at McMaster University and director of the undergraduate Honours Neuroscience Program.