  Variable selection is a key issue when analyzing high-dimensional data. The
explosion of data with large sample sizes and dimensionality brings new
challenges to this problem in both inference accuracy and computational
complexity. To alleviate these problems, we propose a new scalable Markov chain
Monte Carlo (MCMC) sampling algorithm for "large $p$ small $n$" scenarios by
generalizing multiple-try Metropolis to discrete model spaces and further
incorporating neighborhood-based stochastic search. The proof of reversibility
of the proposed MCMC algorithm is provided. Extensive simulation studies are
performed to examine the efficiency of the new algorithm compared with existing
methods. A real data example is provided to illustrate the prediction
performances of the new algorithm.
