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

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Simulation from complex systems, such as proteins, neural networks, andspin-glasses, is one of the most challenging problems in scientificcomputation. The energy landscape of these systems can be characterizedby a multitude of local energy minima separated by high energy barriers. In simulation from these systems, the conventional Markovchain Monte Carlo algorithms, such as the Metropolis-Hastings algorithmand the Gibbs sampler, tend to get trapped in one of local energyminima indefinitely, rendering the simulation ineffective.The goal of this research is to develop an effective Monte Carloalgorithm for simulation from complex systems, and to apply the newalgorithm to some computational problems in statistics andbioinformatics, including molecular structure prediction, phylogenyestimation, neural network training, combinatorial optimization,optimal design, highest posterior density (HPD) interval construction,model selection, and others. The preliminary results show that thecontour Monte Carlo algorithm, which is proposed in this research,will potentially play a leading role in stochastic optimization inplace of other algorithms, such as simulated annealing and geneticalgorithms.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.