Topic
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.
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01 Jan 2005
347 citations
TL;DR: In this paper, the Monte Carlo maximum likelihood (MCMCMC) method is used to estimate stochastic volatility (SV) models, which can be expressed as a linear state space model with log chi-square disturbances and decompose it into a Gaussian part, constructed by the Kalman filter, and a remainder function whose expectation is evaluated by simulation.
347 citations
TL;DR: The overall complexity of computing mean fields as well as k-point correlations of the random solution is proved to be of log-linear complexity in the number of unknowns of a single Multi-level solve of the deterministic elliptic problem.
Abstract: In Monte Carlo methods quadrupling the sample size halves the error. In simulations of stochastic partial differential equations (SPDEs), the total work is the sample size times the solution cost of an instance of the partial differential equation. A Multi-level Monte Carlo method is introduced which allows, in certain cases, to reduce the overall work to that of the discretization of one instance of the deterministic PDE. The model problem is an elliptic equation with stochastic coefficients. Multi-level Monte Carlo errors and work estimates are given both for the mean of the solutions and for higher moments. The overall complexity of computing mean fields as well as k-point correlations of the random solution is proved to be of log-linear complexity in the number of unknowns of a single Multi-level solve of the deterministic elliptic problem. Numerical examples complete the theoretical analysis.
346 citations
TL;DR: This paper deals with the problem of increasing the efficiency of Monte Carlo calculations by reducing the sample size required to produce estimates of a fixed level of accuracy or to increase the accuracy of the estimates for a fixed cost of computation
Abstract: This paper deals with the problem of increasing the efficiency of Monte Carlo calculations. The methods of doing so permit one to reduce the sample size required to produce estimates of a fixed level of accuracy or, alternatively, to increase the accuracy of the estimates for a fixed cost of computation. Few theorems are known with regard to optimal sampling schemes, but several helpful ideas of very general applicability are available for use in designing Monte Carlo sampling schemes. Three of these ideas are discussed and illustrated in simple cases. These ideas are (1) correlation of samples, (2) importance sampling, and (3) statistical estimation. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
341 citations
TL;DR: In this article, the authors consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value.
Abstract: Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are good estimates of the desired quantities. We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard error is a critical step in assessing the simulation output. We consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We give sufficient conditions for the strong consistency of both methods and investigate their finite-sample properties in various examples.
341 citations