September 2009
It has become routine in many application areas to collect high-dimensional sets of candidate predictors, and there is a need for new methods for searching the massive dimensional model space for promising subsets. Although a number of sparse estimation methods have been proposed, such as the Lasso and elastic net, such methods do not allow for uncertainty in variable selection. An alternative is to use Markov chain Monte Carlo (MCMC) to conduct a stochastic search of the model space, but such methods face major computational challenges as the number of candidate predictors increase. This article proposes a new computational approach based on sequential Monte Carlo, which we refer to as particle stochastic search (PSS). We illustrate PSS through applications to linear regression and probit models.
Keywords: Bayes factor; Marginal inclusion probability; Model averaging; Model uncertainty; Sequential Monte Carlo; Stochastic search variable selection; Subset selection
The manuscript is available in PDF format.