The principles behind the computation of protein-ligand binding free energies by Monte Carlo integration are described in detail. The simulation provides gas-phase binding free energies that can be converted to aqueous energies by solvation corrections. The direct integration simulation has several characteristics beneficial to free-energy calculations. One is that the number of parameters that...

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as Bayesian inference, statistical physics, and machine learning. However, due to the curse of dimensionality, deterministic numerical methods are inefficient in high-dimensional settings. Consequentially, for many practical problems one must resort to Monte Carlo es...

background: iodine brachytherapy sources with low photon energies have been widely used in treating cancerous tumors. dosimetric parameters of brachytherapy sources should be determined according to aapm tg-43u1 recommendations before clinical use. monte carlo codes are reliable tools in calculation of these parameters for brachytherapy sources. materials and methods: dosimetric parameters (dos...

In this paper, the pricing of a European call option on the underlying asset is performed by using a Monte Carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. The proposed approach, applied in Monte Carlo simulation, is based on the Black-Scholes equation which generally def...

Quasi-Monte Carlo methods are designed to improve upon the Monte Carlo method for multidimensional numerical integration by using a more regularly distributed point set than the i.i.d. sample associated with Monte Carlo. Lattice rules are one family of quasi-Monte Carlo methods, originally proposed by Korobov in 1959. In this paper, we explain how randomized lattice rules can be used to constru...

A theoretical analysis of the Monte Carlo method for steady-state semiconductor device simulation, also known as the single-particle Monte Carlo method, is presented. At the outset of the formal treatment is the stationary Boltzmann equation supplemented by boundary conditions, which is transformed into an integral equation. The conjugate equation has been formulated in order to develop forward...

We introduce a class of functions in high dimensions which have themaximum effective dimension, then prove that generalized Sobol’sequences provide theO(N−1) convergence rate for the integration of this class of functions. An important consequence is that high-dimensional problems for which quasi-Monte Carlo outperforms Monte Carlo are not necessarily of low-effective dimension. © 2005 Elsevier...

An adaptive Monte Carlo strategy for computing global Sobol ́ sensitivity indices has been presented and discussed. The experimental scheme including an approximation tool, variance-based approaches for sensitivity analysis and Monte Carlo technique for multidimensional integration has been described and studied.

Quasi-Monte Carlo methods are based on the idea that random Monte Carlo techniques can often be improved by replacing the underlying source of random numbers with a more uniformly distributed deterministic sequence. Quasi-Monte Carlo methods often include standard approaches of variance reduction, although such techniques do not necessarily directly translate. In this paper we present a quasi-M...

Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the ada...