Cabras, Stefano2021-06-082021-06-082020-09Cabras, S. (2020). A Dirichlet Process Prior Approach for Covariate Selection. Entropy, 22(9), 948.1099-4300https://hdl.handle.net/10016/32849This article belongs to the Special Issue Bayesian Inference and ComputationThe variable selection problem in general, and specifically for the ordinary linear regression model, is considered in the setup in which the number of covariates is large enough to prevent the exploration of all possible models. In this context, Gibbs-sampling is needed to perform stochastic model exploration to estimate, for instance, the model inclusion probability. We show that under a Bayesian non-parametric prior model for analyzing Gibbs-sampling output, the usual empirical estimator is just the asymptotic version of the expected posterior inclusion probability given the simulation output from Gibbs-sampling. Other posterior conditional estimators of inclusion probabilities can also be considered as related to the latent probabilities distributions on the model space which can be sampled given the observed Gibbs-sampling output. This paper will also compare, in this large model space setup the conventional prior approach against the non-local prior approach used to define the Bayes Factors for model selection. The approach is exposed along with simulation samples and also an application of modeling the Travel and Tourism factors all over the world.9eng© 2020 by the author.Atribución 3.0 EspañaConventional priorsCovariate inclusion probabilityDirichlet process priorNon-local priorOrdinary linear regressionVariable selectionresearch articleEstadísticahttps://doi.org/10.3390/E22090948open access9489Entropy22AR/0000027470