The performance of annealed sequential Monte Carlo sampling as a joint variable selection and parameter estimation method in the linear (mixed) model setting

Variable selection is the statistical problem of identifying predictors that explain the variation in a response, which is challenging when the number of candidate predictors is large. Several existing frequentist and Bayesian methods can perform variable selection in high-dimensional settings with reasonable computation times. Modern Bayesian methods focus on sampling models from the posterior distribution on the model space while neglecting the estimation of model coefficients. Annealed sequential Monte Carlo (SMC) sampling is an appealing method that provides a weighted sample of models and model parameters simultaneously, thus simultaneously performing selection and estimation without further computational effort. We examine the selection and estimation performance of annealed SMC sampling for linear regression and mixed-effects models under different conditions to determine factors that impact its efficacy. We demonstrate that sample size, signal-to-noise ratio, the proportion of important predictors, the correlation of predictors, and the inclusion of a random effect appreciably impact the performance of annealed SMC sampling.