During the past five decades, Markov chain Monte Carlo (MCMC) methods have been developed as a versatile and powerful tool for scientific computing. However, as known by many researchers, conventional MCMC methods are prone to get trapped in local energy minima in simulations from a system with a rugged energy landscape, rendering the simulations inefficient. To overcome this difficulty, the investigaor and his collaborators recently proposed a non-Markov chain Monte Carlo algorithm, the so-called stochastic approximation Monte Carlo (SAMC) algorithm. Extensive numerical results show that SAMC can outperform its MCMC competitors for many hard computational problems, such as molecular structure prediction, phylogenetic tree reconstruction, and complex model selection problems. This project continues to develop SAMC in both theory and methodology. First, SAMC is generalized by allowing some statistical smoothing techniques to be used in iterations to improve its efficiency. A rigorous theory is established concerning the convergence and asymptotic behavior of the generalized algorithm. Second, SAMC is generalized by changing its current discrete setting to continuous one. The resulting algorithm is particularly suitable for solving marginal density estimation problems. Third, SAMC is further improved by making use of some techniques developed in evolutionary computing. Preliminary results show that the performance of SAMC can be significantly improved by the new developments.
This project provides some advanced computational methods, which can play an important role in solving some hard scientific problems, such as molecular structure prediction, phylogeny analysis, genetic network inference, machine learning, and VLSI design. Successful computation to these problems in turn enhances people's understanding to them. This project has broader impacts in both communities of statistical theory and scientific computing. The research results are disseminated to these communities via PI's direct collaboration with researchers in other disciplines, conference presentations, books, and papers published in academic journals. This project has also significant impacts on education through direct involvement of graduate students and incorporation of results into undergraduate and graduate courses.
