Bayesian Evaluation of Informative Hypotheses

This book provides an overview of the developments in the area of Bayesian evaluation of informative hypotheses that took place since the publication of the ?rst paper on this topic in 2001 [Hoijtink, H. Con?rmatory latent class analysis, model selection using Bayes factors and (pseudo) likelihood ratio statistics. Multivariate Behavioral Research, 36, 563588]. The current state of a?airs was presented and discussed by the authors of this book during a workshop in Utrecht in June 2007. Here we would like to thank all authors for their participation, ideas, and contributions. We would also like to thank Sophie van der Zee for her editorial e?orts during the construction of this book. Another word of thanks is due to John Kimmel of Springer for his con?dence in the editors and authors. Finally, we would like to thank the Netherlands Organization for Scienti?c Research (NWO) whose VICI grant (453-05-002) awarded to the ?rst author enabled the organization of the workshop, the writing of this book, and continuation of the research with respect to Bayesian evaluation of informative hypotheses.

This book provides a step-by-step explanation aimed mainly at social scientists, of how to formulate and evaluate a set of informative hypotheses (including references to software). It is a comprehensive book that can easily be accessed by social scientists introducing and elaborating the approach from a philosophical, statistical and psychological point of view.

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This book presents an alternative for traditional null hypothesis testing. It builds on the idea that researchers usually have more informative research-questions than the "nothing is going on" null hypothesis, or the "something is going on" alternative hypothesis. To be more precise, researchers often express their expectations in terms of expected orderings in parameters, for instance, in group means. This book introduces a novel approach, wherein theories or expectations of empirical researchers are translated into one or more so-called informative hypotheses, i.e., hypotheses imposing inequality constraints on (some of) the model parameters. As a consequence, informative hypotheses are much closer to the actual questions researchers have and therefore make optimal use of the data to provide more informative answers to these questions.

A Bayesian approach is used for the evaluation of informative hypotheses and is introduced at a non-technical level in the context of analysis of variance models. Technical aspects of Bayesian evaluation of informative hypotheses are also considered and different approaches are presented by an international group of Bayesian statisticians. Furthermore, applications in a variety of statistical models including among others latent class analysis and multi-level modeling are presented, again at a non-technical level. Finally, the proposed method is evaluated from a psychological, statistical and philosophical point of view.

This book contains numerous illustrations, all in the context of psychology. The proposed methodology, however, is equally relevant for research in other social sciences (e.g., sociology or educational sciences), as well as in other disciplines (e.g., medical or economical research).

The editors are all affiliated at the faculty of Social Sciences at Utrecht University in the Netherlands. Herbert Hoijtink is a professor in applied Bayesian statistics at the Department of Methodology and Statistics. Irene Klugkist is assistant professor at the same department, and Paul A. Boelen is assistant professor at the Department of Clinical and Health Psychology.

Contenu
An Introduction to Bayesian Evaluation of Informative Hypotheses.- An Introduction to Bayesian Evaluation of Informative Hypotheses.- Bayesian Evaluation of Informative Hypotheses.- Illustrative Psychological Data and Hypotheses for Bayesian Inequality Constrained Analysis of Variance.- Bayesian Estimation for Inequality Constrained Analysis of Variance.- Encompassing Prior Based Model Selection for Inequality Constrained Analysis of Variance.- An Evaluation of Bayesian Inequality Constrained Analysis of Variance.- A Further Study of Prior Distributions and the Bayes Factor.- Bayes Factors Based on Test Statistics Under Order Restrictions.- Objective Bayes Factors for Informative Hypotheses: Completing the Informative Hypothesis and Splitting the Bayes Factors.- The Bayes Factor Versus Other Model Selection Criteria for the Selection of Constrained Models.- Bayesian Versus Frequentist Inference.- Beyond Analysis of Variance.- Inequality Constrained Analysis of Covariance.- Inequality Constrained Latent Class Models.- Inequality Constrained Contingency Table Analysis.- Inequality Constrained Multilevel Models.- Evaluations.- A Psychologist's View on Bayesian Evaluation of Informative Hypotheses.- A Statistician's View on Bayesian Evaluation of Informative Hypotheses.- A Philosopher's View on Bayesian Evaluation of Informative Hypotheses.