Bayesian model selection and parameter estimation in penalized regression model using SMC samplers

Penalized regression methods have received a great deal of attention in recent years, mostly through frequentist models using ℓ₁-regularization. However, all existing works assume that the design matrix, that links the explanatory variables to the observed response, is known a priori. Unfortunately, this is often not the case and thus solving this challenging problem is of considerable interest. In this paper, we look at a fully Bayesian formulation of this problem. This paper proposes the use of Sequential Monte Carlo samplers for joint model selection and parameter estimation. Furthermore, a new class of priors based on α-stable family distribution is proposed as non-convex penalty for regularization of the regression coefficients. The performance of the proposed methodology is demonstrated in two different settings.