Mathematical Psychology

by

Parker Smith, Yanjun Liu, James T. Townsend, Trish van Zandt

• LAST MODIFIED: 29 July 2020
• DOI: 10.1093/obo/9780199828340-0266

Introduction

Mathematical psychology is that branch of psychology focusing on the use of mathematical and computational models to explain and predict human behavior. Typical areas of interest are memory, attention, problem solving, perception, decision making, and motor control. The field developed from the measurement problems encountered in psychophysics with a focus on behavioral responses. It has evolved with improvements in technology such as advanced computer systems and brain imaging systems, which have spurred the growth of neuroscience. As the number of tools for research in the field grows, the sophistication and complexity of models have grown. However, a unique characteristic of mathematical psychology is its potential role in all branches of psychology. All “substantive” areas of psychology (e.g., clinical, social, and developmental) could have both empirical and mathematical foundations. As the field grows in complexity and nuance, it is making more and more contributions in these wider areas.

Textbooks and Central Texts

There are a number of important textbooks that, while old, are still used in the early 21st century to teach mathematical psychology at the graduate level, and that are still used as important references. Newer texts include historical surveys and modern computational approaches that were not in practice when mathematical psychology became recognized as a distinct discipline. Batchelder, et al. 2016 updates Luce, et al. 1963. Luce, et al. 1963 was the first, classic attempt to review the literature on mathematical psychology and present mathematical psychology as a unified discipline. Batchelder, et al. 2016 provides a comprehensive summary of modern mathematical psychology. Busemeyer, et al. 2015 gives another comprehensive review of modern mathematical psychology. Laming 1973 is a review of mathematical psychology narrowly focused on questions arising in the modeling of memory, but providing a comprehensive presentation of the problem of information accumulation in simple choice, a problem that drives much of modern research in cognition. Restle and Greeno 1970 is a less well known textbook in which the presentation of materials is strongly influenced by behaviorism and mathematical learning theory. Coombs, et al. 1970 is the first textbook accessible to undergraduates, which remains an important historical reference that includes a number of important foundational topics.

• Batchelder, W. H., H. Colonius, E. Dzhafarov, and J. I. Myung, eds. 2016. New handbook of mathematical psychology. Vols. 1–2. Cambridge, UK: Cambridge Univ. Press.

  An updated edition of Luce et al.’s 1963 classic Handbook of Mathematical Psychology that presents the discipline of mathematical psychology in a modern context.

• Busemeyer, J. R., and A. Diederich. 2010. Cognitive modeling. Los Angeles: SAGE.

  An introductory textbook dealing with specific issues involved in the construction and evaluation of models for cognitive psychology.

• Busemeyer, J. R., Z. Wang, J. T. Townsend, and A. Eidels. 2015. The Oxford handbook of computational and mathematical psychology. New York: Oxford Univ. Press.

  Another comprehensive review of modern mathematical psychology.

• Coombs, C. H., R. M. Dawes, and A. Tversky. 1970. Mathematical psychology: An elementary introduction. Oxford: Prentice-Hall.

  The first textbook on mathematical psychology, it is an important historical reference that includes a number of important foundational topics.

• Laming, D. R. J. 1973. Mathematical psychology. London: Academic Press.

  Another foundational reference, not as broad as other texts of its time, but with more treatment of information accumulation topics and problems involved with modeling of memory.

• Luce, R. D., R. R. Bush, and E. Galanter, eds. 1963. Handbook of mathematical psychology. Vol. 1. Oxford: John Wiley.

  The first, classic attempt to review the literature on mathematical psychology and present mathematical psychology as a unified discipline.

• Restle, F., and J. G. Greeno. 1970. Introduction to mathematical psychology. Oxford: Addison-Wesley.

  A less well known textbook in which the presentation of materials is strongly influenced by behaviorism and mathematical learning theory.