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

蛋白质、神经网络和自旋玻璃等复杂系统的模拟是科学计算中最具挑战性的问题之一。这些系统的能量格局可以用被高能量屏障隔开的大量局部能量极小值来描述。针对传统的马尔可夫链蒙特卡罗算法，如Metropolis-Hastings算法和Gibbs采样器在模拟复杂系统时容易陷入局部能量极小，导致模拟效果不佳的问题，提出一种有效的蒙特卡罗算法，并将其应用于统计和生物信息学中的一些计算问题，包括分子结构预测、系统发育估计、神经网络训练、组合优化、最优设计、最高后验密度(HPD)区间构造、模型选择等。初步研究结果表明，本文提出的等值蒙特卡罗算法有可能取代模拟退火法、遗传算法等其他算法在随机优化中发挥主导作用，在生物、工程、社会科学等领域具有广泛的应用前景。这些算法在确定应用科学中最优化问题的最佳解决方案方面非常强大。学生、研究人员和统计用户，如计算生物学家和计算机科学家，将从这项研究中受益。

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.