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.

Weighted monte carlo: a new technique for calibrating asset-pricing models

Abstract: A general approach for calibrating Monte Carlo models to the market prices of benchmark securities is presented. Starting from a given model for market dynamics (price diffusion, rate diffusion, etc.), the algorithm corrects for price-misspecifications and finite-sample effects in the simulation by assigning “probability weights” to the simulated paths. The choice of weights is done by minimizing the Kullback-Leibler relative entropy distance of the posterior measure to the empirical measure. The resulting ensemble prices the given set of benchmark instruments exactly or in the sense of least-squares. We discuss pricing and hedging in the context of these weighted Monte Carlo models. A significant reduction of variance is demonstrated theoretically as well as numerically. Concrete applications to the calibration of stochastic volatility models and term-structure models with up to forty benchmark instruments are presented. The construction of implied volatility surfaces and forward-rate curves and the pricing and hedging of exotic options are investigated through several examples.

Path integral simulations of atomic and molecular systems

Abstract: The path integral picture of the statistical mechanics of quantum many-body systems is presented from the point of view of developing simulation algorithms. Monte Carlo and molecular dynamics techniques for systems of distinguishable quantum particles, bosons and fermions are reviewed. Path integral simulations of atomic liquids and solids, quantum clusters and solvated electrons are described and the usefulness of such techniques for understanding phenomena such as orientational transitions, surface adsorption and rates of quantum processes is discussed.

A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models

Abstract: This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.

Million-body star cluster simulations: Comparisons between Monte Carlo and direct N-body

Abstract: We present the first detailed comparison between million-body globular cluster simulations computed with a Henon-type Monte Carlo code, CMC, and a direct N-body code, NBODY6++GPU. Both simulations start from an identical cluster model with 106 particles, and include all of the relevant physics needed to treat the system in a highly realistic way. With the two codes 'frozen' (no fine-tuning of any free parameters or internal algorithms of the codes) we find good agreement in the overall evolution of the two models. Furthermore, we find that in both models, large numbers of stellar-mass black holes (> 1000) are retained for 12 Gyr. Thus, the very accurate direct N-body approach confirms recent predictions that black holes can be retained in present-day, old globular clusters. We find only minor disagreements between the two models and attribute these to the small-N dynamics driving the evolution of the cluster core for which the Monte Carlo assumptions are less ideal. Based on the overwhelming general agreement between the two models computed using these vastly different techniques, we conclude that our Monte Carlo approach, which is more approximate, but dramatically faster compared to the direct N-body, is capable of producing an accurate description of the long-term evolution of massive globular clusters even when the clusters contain large populations of stellar-mass black holes.

Monte Carlo Confidence Intervals for Complex Functions of Indirect Effects

Abstract: One challenge in mediation analysis is to generate a confidence interval (CI) with high coverage and power that maintains a nominal significance level for any well-defined function of indirect and direct effects in the general context of structural equation modeling (SEM). This study discusses a proposed Monte Carlo extension that finds the CIs for any well-defined function of the coefficients of SEM such as the product of k coefficients and the ratio of the contrasts of indirect effects, using the Monte Carlo method. Finally, we conduct a small-scale simulation study to compare CIs produced by the Monte Carlo, nonparametric bootstrap, and asymptotic-delta methods. Based on our simulation study, we recommend researchers use the Monte Carlo method to test a complex function of indirect effects.