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Bayesian selection of multiresponse nonlinear regression model

Abstract : A Bayesian method for the selection and ranking of multiresponse nonlinear regression models in a given model set is proposed. It uses an expected utility criterion based on the logarithmic score of a posterior predictive density of each model. Two approaches are proposed to get this posterior. The first is based on a general asymptotically convergent approximation of the model parameter posterior corresponding to a wide class of parameter priors. The second, a numerical one, uses well-known pure or hybrid MCMC methods. Both posterior approximation approaches allow the practical computation of the expected utility criterion on a sample-reuse basis. This leads to a class of Bayesian cross-validation (CV) procedures, aiming at finding the model having the best predictive ability among a set of models. Varied comparisons of the performances of the Bayesian procedures, with that of AIC, BIC and standard CV procedures, are proposed on a simulated and a real model selection problem case studies, of low and high parametric dimensions respectively.
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Submitted on : Wednesday, September 4, 2013 - 10:02:52 AM
Last modification on : Saturday, October 9, 2021 - 4:07:38 AM

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Vivien Rossi, Jean-Pierre Vila. Bayesian selection of multiresponse nonlinear regression model. Statistics, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2008, 42 (4), pp.291-311. ⟨10.1080/02331880701739824⟩. ⟨hal-00857812⟩



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