Statistica Sinica 25 (2015), 1009-1023

OBJECTIVE BAYESIAN HYPOTHESIS TESTING IN

BINOMIAL REGRESSION MODELS WITH

INTEGRAL PRIOR DISTRIBUTIONS

D. Salmer´on, J. A. Cano and C. P. Robert

CIBER Epidemiolog´ıa y Salud P´ublica (CIBERESP), Universidad de Murcia

and PSL, Universit´e Paris-Dauphine

Abstract: In this work we apply the methodology of integral priors to deal with Bayesian model selection in nested binomial regression models with a general link function. These models are often used to investigate associations and risks in epidemiological studies where one goal is to find whether or not an exposure is a risk factor for developing a certain disease; the purpose of the current paper is to test the effect of specific exposure factors. We formulate the problem as a Bayesian model selection one and solve it using objective Bayes factors. To elicit prior distributions on the regression coefficients of the binomial regression models, we rely on the methodology of integral priors that is nearly automatic as it only requires the specification of estimation reference priors and it does not depend on tuning parameters or on hyperparameters.

Key words and phrases: Binomial regression models, integral priors, Jeffreys prior, Markov chain, objective Bayes factors.