A Contour Based Monte Carlo Algorithm with Applications to Computational Statistics and Bioinformatics

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

Simulation from complex systems, such as proteins, neural networks, and spin-glasses, is one of the most challenging problems in scientific computation. The energy landscape of these systems can be characterized by a multitude of local energy minima separated by high energy barriers. In simulation from these systems, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis-Hastings algorithm and the Gibbs sampler, tend to get trapped in one of local energy minima indefinitely, rendering the simulation ineffective. The goal of this research is to develop an effective Monte Carlo algorithm for simulation from complex systems, and to apply the new algorithm to some computational problems in statistics and bioinformatics, including molecular structure prediction, phylogeny estimation, neural network training, combinatorial optimization, optimal design, highest posterior density (HPD) interval construction, model selection, and others. The preliminary results show that the contour Monte Carlo algorithm, which is proposed in this research, will potentially play a leading role in stochastic optimization in place of other algorithms, such as simulated annealing and genetic algorithms. In this research algorithms are developed that are potentially useful in many fields such as biology, engineering, and the social sciences. These algorithms are powerful in identifying best solutions to optimization problems in applied sciences. Students, researchers, and users of statistics, such as computational biologists and computer scientists, will benefit from this research.