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The Society for Mathematical Psychology promotes the advancement and communication of research in mathematical psychology and related disciplines. Mathematical psychology is broadly defined to include work of a theoretical character that uses mathematical methods, formal logic, or computer simulation. The official journals of the society are Journal of Mathematical Psychology and Computational Brain & Behavior.

Bayesian Statistics for Experimental Scientists

A new book about Bayesian statistics is now available for purchase from MIT Press. The book is titled Bayesian Statistics for Experimental Scientists: A General Introduction Using Distribution-Free Methods. The book is a novel introduction to Bayesian statistics with a special emphasis on distribution-free or nonparametric procedures.

Although the book is designed for experimental scientists in general, there are a number of applications associated with either the estimation of parameters or the testing of models from mathematical psychology. There are nonstandard analyses and methods in the book that should be of interest to mathematical psychologists, yet the book is written with either an advanced undergraduate student or a graduate student in experimental science in mind. I have in fact used a draft version of the book to teach a required graduate course at Tufts University in advanced statistics for psychologists.

The book provides R programming instructions for implementing all the methods, and there are many exercises at the end of each chapter. The book is organized in two parts. Part I provides a general introduction to probability theory, the binomial model, multinomial models, and experimental comparisons with categorical variables. Part II deals with techniques for the analysis of rank-based data. Topics included in Part II are rank-based experimental tests, the Wilcoxon signed-rank procedure, the Mann-Whitney method, the Goodman-Kruskal statistic, the goodness-of-fit of a mathematical function to data, and the Kendall tau correlation. There are side-by-side comparisons made in all parts of the book between frequentist and Bayesian methods. The discussion in several chapters provides a critique of frequentist practice and demonstrates why the Bayesian approach is better suited to the goals of experimental scientists.

 
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