On the safe use of prior densities for Bayesian model selection

Abstract

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depends on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well-known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real-world application on exoplanet detection.

accepted in WIREs Computational Statistics (to appear)

References in corpus (9)

• The formal definition of reference priors
• Criteria for Bayesian model choice with application to variable selection
• Observational constraints on cosmological solutions of $f(Q)$ theories
• Cooperative Parallel Particle Filters for online model selection and applications to Urban Mobility
• Bilby-MCMC: An MCMC sampler for gravitational-wave inference
• HADES RV program with HARPS-N at TNG. IX. A super-Earth around the M dwarf Gl686
• Two Jovian planets around the giant star HD202696. A growing population of packed massive planetary pairs around massive stars?
• Prior knowledge elicitation: The past, present, and future
• A Bayesian inference and model selection algorithm with an optimisation scheme to infer the model noise power

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