Browsing by Subject "Integral priors"

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    Integral priors and constrained imaginary training samples for nested and non-nested Bayesian model Comparison
    (International Society for Bayesian Analysis, 2013-06) Cano JA; Salmerón D; Ciencias Sociosanitarias
    In Bayesian model selection when the prior information on the parameters of the models is vague default priors should be used. Unfortunately, these priors are usually improper yielding indeterminate Bayes factors that preclude the comparison of the models. To calibrate the initial default priors Cano et al. (2008) proposed integral priors as prior distributions for Bayesian model selection. These priors were defined as the solution of a system of two integral equations that under some general assumptions has a unique solution associated with a recurrent Markov chain. Later, in Cano et al. (2012b) integral priors were successfully applied in some situations where they are known and they are unique, being proper or not, and it was pointed out how to deal with other situations. Here, we present some new situations to illustrate how this new methodology works in the cases where we are not able to explicitly find the integral priors but we know they are proper and unique (one-sided testing for the exponential distribution) and in the cases where recurrence of the associated Markov chains is difficult to check. To deal with this latter scenario we impose a technical constraint on the imaginary training samples space that virtually implies the existence and the uniqueness of integral priors which are proper distributions. The improvement over other existing methodologies comes from the fact that this method is more automatic since we only need to simulate from the involved models and their posteriors to compute very well behaved Bayes factors.
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    On integral priors for multiple comparison in Bayesian model selection
    (Wiley, 2026-02-16) Salmerón Martínez, Diego; Cano, Juan Antonio; Robert, Christian P.; Ciencias Sociosanitarias; Facultades de la UMU::Facultad de Medicina
    Noninformative priors constructed for estimation purposes are usually not appropriate for model selection and testing. The methodology of integral priors was developed to get prior distributions for Bayesian model selection when comparing two models, modifying initial improper reference priors. We propose a generalisation of this methodology to more than two models. Our approach adds an artificial copy of each model under comparison by compactifying the parametric space and creating an ergodic Markov chain across all models that returns the integral priors as marginals of the stationary distribution. Besides the guarantee of their existence and the lack of paradoxes attached to estimation reference priors, an additional advantage of this methodology is that the simulation of this Markov chain is straightforward as it only requires simulations of imaginary training samples for all models and from the corresponding posterior distributions. We present some examples, including situations where other methodologies need specific adjustments or do not produce a satisfactory answer.