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.

Monte Carlo study of the isotropic and nematic phases of infinitely thin hard platelets

Abstract: We present the results of a detailed Monte Carlo study of the phase diagram of infinitely thin hard platelets. A weak first order isotropicnematic transition is observed. The equation of state in the isotropic regime is compared with several current theories, none of which is found to be fully satisfactory. The density dependence of the nematic order parameter is found to be compatible with a ‘critical’ exponent β=0·25. A study of the fluctuations of the order parameter in the isotropic phase casts doubt on the applicability of the Landau-de Gennes expression for the free energy. We observe that the relation between the nematic order parameters and is compatible with the predictions of mean-field theory. Practical aspects of the computation are discussed. A novel method to compute the pressure in a constant-volume Monte Carlo run is presented.

Multilevel Monte Carlo methods

Abstract: The author’s presentation of multilevel Monte Carlo path simulation at the MCQMC 2006 conference stimulated a lot of research into multilevel Monte Carlo methods. This paper reviews the progress since then, emphasising the simplicity, flexibility and generality of the multilevel Monte Carlo approach. It also offers a few original ideas and suggests areas for future research.

Introduction to Monte Carlo methods

Abstract: This chapter describes a sequence of Monte Carlo methods: importance sampling, rejection sampling, the Metropolis method, and Gibbs sampling. For each method, we discuss whether the method is expected to be useful for high—dimensional problems such as arise in inference with graphical models. After the methods have been described, the terminology of Markov chain Monte Carlo methods is presented. The chapter concludes with a discussion of advanced methods, including methods for reducing random walk behaviour.

Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm

Abstract: Summary. Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed) sampling to construct Monte Carlo approximations at the E-step. One approach involves generating random samples from the exact conditional distribution of the random effects (given the data) by rejection sampling, using the marginal distribution as a candidate. The second method uses a multivariate t importance sampling approximation. In many applications the two methods are complementary. Rejection sampling is more efficient when sample sizes are small, whereas importance sampling is better with larger sample sizes. Monte Carlo approximation using random samples allows the Monte Carlo error at each iteration to be assessed by using standard central limit theory combined with Taylor series methods. Specifically, we construct a sandwich variance estimate for the maximizer at each approximate E-step. This suggests a rule for automatically increasing the Monte Carlo sample size after iterations in which the true EM step is swamped by Monte Carlo error. In contrast, techniques for assessing Monte Carlo error have not been developed for use with alternative implementations of Monte Carlo EM algorithms utilizing Markov chain Monte Carlo E-step approximations. Three different data sets, including the infamous salamander data of McCullagh and Nelder, are used to illustrate the techniques and to compare them with the alternatives. The results show that the methods proposed can be considerably more efficient than those based on Markov chain Monte Carlo algorithms. However, the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension.

Two-Step Estimation of a Censored System of Equations

Abstract: A consistent two-step estimation procedure is proposed for a system of equations with limited dependent variables. Monte Carlo simulation results suggest the procedure outperforms an existing two-step method.