Adaptive MC³ and Gibbs algorithms for Bayesian Model Averaging in Linear Regression Models

2013/06/25 by Demetris Lamnisos, Lamnisos, Demetris, Jim E. Griffin +3
Computer Science · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #stat.CO

paper · pdf · doi:10.48550/arxiv.1306.6028

arxiv created 2013/06/25 · openalex publication_date 2013/06/25 · arxiv updated 2013/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The MC³ (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997) samplers are the most widely implemented algorithms for Bayesian Model Averaging (BMA) in linear regression models. These samplers draw a variable at random in each iteration using uniform selection probabilities and then propose to update that variable. This may be computationally inefficient if the number of variables is large and many variables are redundant. In this work, we introduce adaptive versions of these samplers that retain their simplicity in implementation and reduce the selection probabilities of the many redundant variables. The improvements in efficiency for the adaptive samplers are illustrated in real and simulated datasets.

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