Search Results for « Monte Carlo methods »

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

An introductory review of the Monte Carlo method for the statistical mechanics of condensed matter systems is given. Basic principles (random number generation, simple sampling versus importance sampling, Markov chains and master equations, etc) are explained and some classical applications (self-avoiding walks, percolation, the Ising model) are sketched. The finite-size scaling analysis of both second- and first-order phase transitions is described in detail, and also the study of surface and interfacial phenomena as well as the choice of appropriate boundary conditions is discussed. Only brief comments are given on topics such as applications to dynamic phenomena, quantum problems, and recent algorithmic developments (new sampling schemes based on reweighting techniques, nonlocal updating, parallelization, etc). The techniques described are exemplified with many illustrative applications.

Attention is focused on the application of the Monte Carlo method to particle transport problems, with emphasis on neutron and photon transport. Topics covered include sampling methods, mathematical prescriptions for simulating particle transport, mechanics of simulating particle transport, neutron transport, and photon transport. A literature survey of 204 references is included. (GMT)

Since the beginning of electronic computing, people have been interested in carrying out random experiments on a computer. Such Monte Carlo techniques are now an essential ingredient in many quantitative investigations. Why is the Monte Carlo method ( MCM ) so important today? This article explores the reasons why the MCM has evolved from a ‘last resort’ solution to a leading methodology that permeates much of contemporary science, finance, and engineering. WIREs Comput Stat 2014, 6:386–392. doi: 10.1002/wics.1314 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical Models > Simulation Models

The Monte Carlo method is a wide spread numerical method which is used in a lot of different areas of numerical calculations.This thesis gives a short introduction to the method.In the introduction we give a short resume and history of the method.One area of major interest in the use of Monte Carlo methods is the generation of random numbers and sampling from given distribution functions; this is discussed in the next chapters.Then follows a description of the method and various aspects of the performance are discussed.Variance reduction plays a big role in the Monte Carlo theory and the most common topics are covered.To illustrate the use of Monte Carlo methods we give some examples of applications from the domain of particle transport.A revision of probability theory and an mathematical justification of the method is included in the appendices.

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10--20 times speedup.