New Handbook of Mathematical Psychology: Volume 1, Foundations and Methodology

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 in both traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the first title in this field to be published, 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. This first volume focuses on select mathematical ideas, theories, and modeling approaches to form a foundational treatment of mathematical psychology.

1. Selected concepts from probability Hans Colonius; 2. Probability, random variables, and selectivity Ehtibar N. Dzhafarov and Janne V. Kujala; 3. Functional equations Che Tat Ng; 4. Knowledge spaces and learning spaces Jean-Paul Doignon and Jean-Claude Falmagne; 5. Network analysis John P. Boyd and William H. Batchelder; 6. Evolutionary game theory J. McKenzie Alexander; 7. Choice, preference, and utility: probabilistic and deterministic representations Anthony A. J. Marley and Michel Regenwetter; 8. Discrete state models of cognition William H. Batchelder; 9. Bayesian hierarchical models Jeffrey N. Rouder, Richard D. Morey and Michael S. Pratte; 10. Model evaluation and selection Jay Myung, Daniel R. Cavagnaro and Mark A. Pitt.

William H. Batchelder is Professor of Cognitive Sciences at the University of California, Irvine.
Hans Colonius is Professor of Psychology at Carl V. Ossietzky Universität Oldenburg, Germany.
Ehtibar N. Dzhafarov is Professor of Psychological Sciences at Purdue University, Indiana.
Jay Myung is Professor of Psychology at Ohio State University.