# New Handbook of Mathematical Psychology

Book Preface

About mathematical psychology

There are three fuzzy and interrelated understandings of what mathematical psychology is: part of mathematics, part of psychology, and analytic methodology. We call them “fuzzy” because we do not offer a rigorous way of defining them. As a rule, a work in mathematical psychology, including the chapters of this handbook, can always be argued to conform to more than one if not all three of these understandings (hence our calling them “interrelated”). Therefore, it seems safer to think of them as three constituents of mathematical psychology that may be differently expressed in any given line of work.

**Contents**

List of contributors page vii

Preface

william h. batchelder, hans colonius,

ehtibar n. dzhafarov, and jay myung ix

1 Selected concepts from probability hans colonius 1

2 Probability, random variables, and selectivity ehtibar n. dzhafarov and janne kujala 85

3 Functional equations che tat ng 151

4 Network analysis john p. boyd and william h. batchelder 194

5 Knowledge spaces and learning spaces jean-paul doignon and jean-claude falmagne 274

6 Evolutionary game theory j. mckenzie alexander 322

7 Choice, preference, and utility: probabilistic and deterministic representations a. a. j. marley and michel regenwetter 374

8 Discrete state models of cognition william h. batchelder 454

9 Bayesian hierarchical models of cognition jeffrey n. rouder, richard d. morey, and michael s. pratte 504

10 Model evaluation and selection jay myung, daniel r. cavagnaro, and mark a. pitt 552

Index 599

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