Monte Carlo molecular modeling

About: Monte Carlo molecular modeling is a research topic. Over the lifetime, 11307 publications have been published within this topic receiving 409122 citations.

Central Limit Theorem for sequential Monte Carlo methods and its application to Bayesian inference

Abstract: The term “sequential Monte Carlo methods” or, equivalently, “particle filters,” refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (πt). We establish in this paper a central limit theorem for the Monte Carlo estimates produced by these computational methods. This result holds under minimal assumptions on the distributions πt, and applies in a general framework which encompasses most of the sequential Monte Carlo methods that have been considered in the literature, including the resample-move algorithm of Gilks and Berzuini [J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001) 127–146] and the residual resampling scheme. The corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter. We study, in particular, in some typical examples of Bayesian applications, whether and at which rate these asymptotic variances diverge in time, in order to assess the long term reliability of the considered algorithm.

Neumann Expansion for Stochastic Finite Element Analysis

Abstract: With the aid of the finite element method, the present paper deals with the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature. The spatial variabilities are modeled as two‐dimensional stochastic fields. The finite element discretization is performed in such a way that the size of each element is sufficiently small. Then, the present paper takes advantage of the Neumann expansion technique in deriving the finite element solution for the response variability within the framework of the Monte Carlo method. The Neumann expansion technique permits more detailed comparison between the perturbation and Monte Carlo solutions for accuracy, convergence, and computational efficiency. The result from such a Monte Carlo method is also compared with that based on the commonly used perturbation method. The comparison shows that the validity of the perturbation method is limited to the c...

Monte Carlo Methods in Bayesian Computation

Abstract: This is an important contribution to a modern area of applied probability that deals with nonstationary Markov chains in continuous time. This area is becoming increasingly useful in engineering, economics, communication theory, active networking, and so forth, where the Markov-chain system is subject to frequent  uctuations with clusters of states such that the chain  uctuates very rapidly among different states of a cluster but changes less rapidly from one cluster to another. The authors use the setting of singular perturbations, which allows them to study both weak and strong interactions among the states of the chain. This leads to simpliŽ cations through the averaging principle, aggregation, and decomposition. The main results include asymptotic expansions of the corresponding probability distributions, occupations measures, limiting normality, and exponential rates. These results give the asymptotic behavior of many controlled stochastic dynamic systems when the perturbation parameter tends to 0. The classical analytical method employs the asymptotic expansions of onedimensional distributions of the Markov chain as solutions to a system of singularly perturbed ordinary differential equations. Indeed, the asymptotic behavior of solutions of such equations is well studied and understood. A more probabilistic approach also used by the authors is based on the tightness of the family of probability measures generated by the singularly perturbed Markov chain with the corresponding weak convergence properties. Both of these methods are illustrated by practical dynamic optimization problems, in particular by hierarchical production planning in a manufacturing system. An important contribution is the last chapter, Chapter 10, which describes numerical methods to solve various control and optimization problems involving Markov chains. Altogether the monograph consists of three parts, with Part I containing necessary, technically rather demanding facts about Markov processes (which in the nonstationary case are deŽ ned through martingales.) Part II derives the mentioned asymptotic expansions, and Part III deals with several applications, including Markov decision processes and optimal control of stochastic dynamic systems. This technically demanding book may be out of reach of many readers of Technometrics. However, the use of Markov processes has become common for numerous real-life complex stochastic systems. To understand the behavior of these systems, the sophisticated mathematical methods described in this book may be indispensable.

Monte Carlo Particle Transport Methods: Neutron and Photon Calculations

Abstract: With this book we try to reach several more-or-less unattainable goals namely: To compromise in a single book all the most important achievements of Monte Carlo calculations for solving neutron and photon transport problems. To present a book which discusses the same topics in the three levels known from the literature and gives us useful information for both beginners and experienced readers. It lists both well-established old techniques and also newest findings.