Archive for imaginary training sample
integral priors for model comparison [2.0]
Posted in Books, Statistics, University life with tags arXiv, Bayesian inference, Bayesian model choice, Bayesian statistics, ergodicity, imaginary training sample, integral priors, Juan Antonio Cano, Markov chain, MCMC, Murcia, nested models, noninformative priors, reference priors, Spain, Universidad de Murcia on May 2, 2025 by xi'an
integral priors for multiple comparison
Posted in Books, Statistics, University life with tags ergodicity, imaginary training sample, improper posteriors, improper priors, intrinsic Bayes factor, Juan Antonio Cano, Markov chain, noninformative priors, null recurrence, pseudo-Bayes factors, reference priors, transience on June 24, 2024 by xi'an
Diego Salmerón and I just arXived a paper on integral priors for multiple model comparison, about deriving reference priors for multiple hypothesis testing. As (so-called) noninformative priors constructed for estimation purposes are usually not appropriate for model selection and testing due to their improperness, Jeffreys-Lindley paradoxes and the like, the methodology of integral priors was developed to get prior distributions for Bayesian model selection when comparing two models, modifying initial improper reference priors. This paper proposes a generalization of this methodology when than two models are to be compared. In order to avoid the above paradoxes and the associated possibility of producing a null recurrent or transient Markov chain, our approach adds an artificial copy of each model under comparison by compactifying the corresponding parametric space and creates an ergodic Markov chain exploring all models that returns the integral priors as marginals of the ergodic and stationary joint distribution. Besides the guarantee of existence of these integral priors and the disappearance of paradoxes that plague estimation reference priors, an additional perk of this methodology is that the simulation of this Markov chain is straightforward as it only requires simulations of imaginary training samples and from the corresponding posterior distributions, for all models, while producing Bayes factor approximations on the side. This renders its implementation automatic and generic, both in the nested and in the nonnested cases. We associated our late friend Juan Antonio Cano to this paper as he was instrumental in initiating both this collaboration and the methodology at its core.
