New PDF release: Bayesian Evaluation of Informative Hypotheses (Statistics

By Herbert Hoijtink, Irene Klugkist, Paul Boelen

ISBN-10: 0387096116

ISBN-13: 9780387096117

ISBN-10: 1441918744

ISBN-13: 9781441918741

This e-book presents an summary of the advancements within the region of Bayesian evaluate of informative hypotheses that came about because the e-book of the ?rst paper in this subject in 2001 [Hoijtink, H. Con?rmatory latent category research, version choice utilizing Bayes elements and (pseudo) probability ratio facts. Multivariate Behavioral learn, 36, 563–588]. the present nation of a?airs was once provided and mentioned via the authors of this e-book in the course of a workshop in Utrecht in June 2007. the following we want to thank all authors for his or her participation, rules, and contributions. we might additionally wish to thank Sophie van der Zee for her editorial e?orts throughout the development of this e-book. one other be aware of thank you is because of John Kimmel of Springer for his con?dence within the editors and authors. eventually, we want to thank the Netherlands association for Scienti?c study (NWO) whose VICI supply (453-05-002) provided to the ?rst writer enabled the association of the workshop, the writing of this publication, and continuation of the learn with admire to Bayesian overview of informative hypotheses.

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Additional resources for Bayesian Evaluation of Informative Hypotheses (Statistics for Social and Behavioral Sciences)

Example text

The outcome variable Recognition is measured on a scale with a range of possible scores between 0 and 15. 1. Also, the sample mean (M ) and sample standard deviation (SD) are provided. It is assumed that the data are normally distributed with a mean µ and variance σ 2 . Both in classical and Bayesian approaches, a key element of any analysis is the function that represents the information in the data with respect to the model parameters. This is called the likelihood function. It is a formal representation of the knowledge with respect to µ and σ 2 contained in the data.

There are two drawbacks of multiple hypothesis testing: It is hard to control both the type I and type II errors and results obtained using multiple hypothesis testing may be mutually inconsistent. In the following chapters it will be shown that it is relatively easy to evaluate a set of informative hypotheses using Bayesian inequality constrained analysis of variance. The use of inequality constraints is not limited to analysis of variance type models. In the third part of the book it will be shown how inequality constrained hypotheses can be formulated in the context of analysis of covariance models, latent class models, multilevel models, and models for contingency tables.

1 − µ2 } > {µ3 − µ4 }). Note that the restriction in which the minus sign is replaced by a plus sign is also possible. , µ > 0). This restriction will be used in Chapter 13 of this book, which deals with inequality constrained multilevel analysis. • Mean restricted to be larger than another mean plus a number, for instance, µ1 > {µ2 + 2}. This restriction can be used if researchers want to include a minimally required effect size in their hypotheses; that is, the first mean should be at least 2 larger than the second mean.

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Bayesian Evaluation of Informative Hypotheses (Statistics for Social and Behavioral Sciences) by Herbert Hoijtink, Irene Klugkist, Paul Boelen


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