BayesVarSel: Bayesian Testing, Variable Selection and model averaging in Linear Models using R

This paper introduces the R package BayesVarSel which implements objective Bayesian methodology for hypothesis testing and variable selection in linear models. The package computes posterior probabilities of the competing hypotheses/models and provides a suite of tools, specifically proposed in the literature, to properly summarize the results. Additionally, \ourpack\ is armed with functions to compute several types of model averaging estimations and predictions with weights given by the posterior probabilities. BayesVarSel contains exact algorithms to perform fast computations in problems of small to moderate size and heuristic sampling methods to solve large problems. The software is intended to appeal to a broad spectrum of users, so the interface has been carefully designed to be highly intuititive and is inspired by the well-known lm function. The issue of prior inputs is carefully addressed. In the default usage (fully automatic for the user)BayesVarSel implements the criteria-based priors proposed by Bayarri et al (2012), but the advanced user has the possibility of using several other popular priors in the literature. The package is available through the Comprehensive R Archive Network, CRAN. We illustrate the use of BayesVarSel with several data examples.

[1]  Christina Gloeckner,et al.  Modern Applied Statistics With S , 2003 .

[2]  D. Dey,et al.  A First Course in Linear Model Theory , 2001 .

[3]  A. Zellner,et al.  Posterior odds ratios for selected regression hypotheses , 1980 .

[4]  J. Berger.  The case for objective Bayesian analysis , 2006 .

[5]  M. J. Bayarri,et al.  Criteria for Bayesian model choice with application to variable selection , 2012, 1209.5240.

[6]  J. Berger,et al.  Optimal predictive model selection , 2004, math/0406464.

[7]  Eduardo Ley,et al.  On the Effect of Prior Assumptions in Bayesian Model Averaging With Applications to Growth Regression , 2007 .

[8]  M. Clyde,et al.  Mixtures of g Priors for Bayesian Variable Selection , 2008 .

[9]  L. Wasserman,et al.  A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion , 1995 .

[10]  L. Joseph,et al.  Bayesian Statistics: An Introduction , 1989 .

[11]  E. George,et al.  APPROACHES FOR BAYESIAN VARIABLE SELECTION , 1997 .

[12]  D. Madigan,et al.  Bayesian Model Averaging for Linear Regression Models , 1997 .

[13]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[14]  James G. Scott,et al.  An exploration of aspects of Bayesian multiple testing , 2006 .

[15]  M. J. Bayarri,et al.  Extending conventional priors for testing general hypotheses in linear models , 2007 .

[16]  X. Sala-i-Martin,et al.  Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (Bace) Approach , 2000 .

[17]  M. Steel,et al.  Jointness in Bayesian Variable Selection with Applications to Growth Regression , 2006 .

[18]  A. Zellner,et al.  Basic Issues in Econometrics. , 1986 .

[19]  Laura Deldossi,et al.  Objective Bayesian model discrimination in follow-up experimental designs , 2014, 1405.2818.

[20]  J. Bernardo,et al.  THE FORMAL DEFINITION OF REFERENCE PRIORS , 2009, 0904.0156.

[21]  I. Ehrlich.  Participation in Illegitimate Activities: A Theoretical and Empirical Investigation , 1973, Journal of Political Economy.

[22]  G. García-Donato,et al.  On Sampling Strategies in Bayesian Variable Selection Problems With Large Model Spaces , 2013 .