Multiple-try Stochastic Search for Bayesian Variable Selection

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample size and dimensionality brings new challenges to this problem in both inference efficiency and computational complexity. To alleviate these problems, a scalable Markov chain Monte Carlo (MCMC) sampling algorithm is proposed by generalizing multiple-try Metropolis to discrete model space and further incorporating neighborhood-based stochastic search. In this thesis, we study the behaviors of this MCMC sampler in the "large p small n'' scenario where the number of predictors p is much greater than the number of observations n. Extensive numerical experiments including simulated and real data examples are provided to illustrate its performance. Choices of tunning parameters are discussed.