Bayesian Evidence and Model Selection

In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical techniques. Specific attention is paid to the Laplace approxima...

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Bibliographic Details
Published inarXiv.org
Main Authors Knuth, Kevin H, Habeck, Michael, Malakar, Nabin K, Mubeen, Asim M, Placek, Ben
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.11.2015
Subjects
Bayesian analysis
Importance sampling
Mathematical analysis
Mathematical models
Model testing
Physics - Instrumentation and Methods for Astrophysics
Signal detection
Signal processing
Statistics - Applications
Statistics - Computation
Statistics - Machine Learning
Statistics - Methodology
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Summary:In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical techniques. Specific attention is paid to the Laplace approximation, variational Bayes, importance sampling, thermodynamic integration, and nested sampling and its recent variants. Analogies to statistical physics, from which many of these techniques originate, are discussed in order to provide readers with deeper insights that may lead to new techniques. The utility of Bayesian model testing in the domain sciences is demonstrated by presenting four specific practical examples considered within the context of signal processing in the areas of signal detection, sensor characterization, scientific model selection and molecular force characterization.
ISSN:2331-8422
DOI:10.48550/arxiv.1411.3013