Master thesis

The Highest Posterior Density Posterior Prior for Bayesian Model Selection

During the second year of the Methodology and Statistics researchmaster, I have studied methods of Bayesian model selection using Bayes factors, supervised by Dr. Irene Klugkist and Prof. Herbert Hoijtink. In my master thesis a new type of default prior distribution is proposed that I think generates Bayes Factors that come closest to an expert opinion about model support.

Abstract

In this paper a new type of prior is proposed that could be suitable in the context of model selection using Bayes factors. The Highest Posterior Density Posterior Prior (HPDPP) consists of a uniform distribution over the highest posterior density area, and basically results in truncation of low-density parameter space. The behavior and properties of the new prior are illustrated using constrained analysis of variance models. Both theoretical justification and simulations are used to argue that this prior has attractive properties for model selection. Because the HPDPP only uses relevant parameter space to determine the size of a model, results do not heavily depend on sample size or number of parameters. To avoid complications for interpretation it is recommended only to test exclusive models when using the HPDPP.

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The PDF should be available on website of the UU library, but when it isn't you can grab it here.