Showing papers on "Monte Carlo molecular modeling published in 2019"
TL;DR: The proposed algorithm suggests to divide the big dataset into some smaller subsets and provides a simple method to aggregate the subset posteriors to approximate the full data posterior and is coined as “Double-Parallel Monte Carlo.”
Abstract: This paper proposes a simple, practical, and efficient MCMC algorithm for Bayesian analysis of big data. The proposed algorithm suggests to divide the big dataset into some smaller subsets and provides a simple method to aggregate the subset posteriors to approximate the full data posterior. To further speed up computation, the proposed algorithm employs the population stochastic approximation Monte Carlo algorithm, a parallel MCMC algorithm, to simulate from each subset posterior. Since this algorithm consists of two levels of parallel, data parallel and simulation parallel, it is coined as "Double-Parallel Monte Carlo." The validity of the proposed algorithm is justified mathematically and numerically.
23 citations
TL;DR: In this article, the authors used path integral Monte Carlo (PIMC) simulations to calculate the momentum distribution of the homogeneous electron gas at finite temperature and demonstrated how the restricted PIMC method can be extended to incorporate open paths in order to allow for simulations in fermionic systems where a sign problem is present.
17 citations
TL;DR: In this paper, the authors proposed a hybrid finite difference method with a Monte Carlo boundary condition for solving the Black-Scholes equations, which can be applied to other types of option pricing problems.
Abstract: We propose an accurate, efficient, and robust hybrid finite difference method, with a Monte Carlo boundary condition, for solving the Black–Scholes equations. The proposed method uses a far-field boundary value obtained from a Monte Carlo simulation, and can be applied to problems with non-linear payoffs at the boundary location. Numerical tests on power, powered, and two-asset European call option pricing problems are presented. Through these numerical simulations, we show that the proposed boundary treatment yields better accuracy and robustness than the most commonly used linear boundary condition. Furthermore, the proposed hybrid method is general, which means it can be applied to other types of option pricing problems. In particular, the proposed Monte Carlo boundary condition algorithm can be implemented easily in the code of the existing finite difference method, with a small modification.
16 citations
TL;DR: A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation.
Abstract: In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A...
13 citations
TL;DR: In this paper, the authors developed a computational methodology to simulate the aggregation and fragmentation of particles and developed scaling relations that can be used to decrease the number of primary particles towards minimization of the computation time.
9 citations
20 May 2019
3 citations
Posted Content•
TL;DR: In this article, the authors evaluate the performance of three methods, Straatsma, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness, for the energy time-series given by Diffusion Monte Carlo, Full Configuration Interaction Quantum Monte Carlo and Coupled Cluster Monte Carlo methods.
Abstract: In quantum Monte Carlo (QMC) methods, energy estimators are calculated as the statistical average of the Markov chain sampling of energy estimator along with an associated statistical error. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods, Straatsma, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness, for the energy time-series given by Diffusion Monte Carlo, Full Configuration Interaction Quantum Monte Carlo and Coupled Cluster Monte Carlo methods. From these analyses we describe a hybrid analysis method which provides reliable error estimates for series of all lengths. Equally important is the estimation of the appropriate start point of the equilibrated phase, and two heuristic schemes are tested, establishing that MSER (mean squared error rule) gives reasonable and constant estimations independent of the length of time-series.
2 citations