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http://dx.doi.org/10.29220/CSAM.2019.26.2.217

A tutorial on generalizing the default Bayesian t-test via posterior sampling and encompassing priors  

Faulkenberry, Thomas J. (Department of Psychological Sciences, Tarleton State University)
Publication Information
Communications for Statistical Applications and Methods / v.26, no.2, 2019 , pp. 217-238 More about this Journal
Abstract
With the advent of so-called "default" Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise, requiring the analyst to accept a one-size-fits-all approach to hypothesis testing. Further, such tests may not have the flexibility to test problems the scientist really cares about. In this tutorial, I demonstrate a flexible approach to generalizing one specific default test (the JZS t-test) (Rouder et al., Psychonomic Bulletin & Review, 16, 225-237, 2009) that is becoming increasingly popular in the social and behavioral sciences. The approach uses two results, the Savage-Dickey density ratio (Dickey and Lientz, 1980) and the technique of encompassing priors (Klugkist et al., Statistica Neerlandica, 59, 57-69, 2005) in combination with MCMC sampling via an easy-to-use probabilistic modeling package for R called Greta. Through a comprehensive mathematical description of the techniques as well as illustrative examples, the reader is presented with a general, flexible workflow that can be extended to solve problems relevant to his or her own work.
Keywords
Bayes factors; Bayesian inference; hypothesis testing; MCMC sampling; JZS t-test; Savage-Dickey density ratio; encompassing priors;
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