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Metropolis-adjusted Langevin algorithm

In computational statistics, the Metropolis-adjusted Langevin algorithm (MALA) or Langevin Monte Carlo (LMC) is a Markov chain Monte Carlo (MCMC) method for obtaining random samples – sequences of ran

Diagrammatic Monte Carlo

In mathematical physics, the diagrammatic Monte Carlo method is based on stochastic summation of Feynman diagrams with controllable error bars. It was developed by Boris Svistunov and Nikolay Prokof'e

Monte Carlo method

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use rando

Ziff–Gulari–Barshad model

The Ziff–Gulari–Barshad (ZGB) model is a simple Monte Carlo method for catalytic reactions of oxidation of carbon monoxide to carbon dioxide on a surface using Monte-Carlo methods which captures corre

Monte Carlo localization

Monte Carlo localization (MCL), also known as particle filter localization, is an algorithm for robots to localize using a particle filter. Given a map of the environment, the algorithm estimates the

Ensemble Kalman filter

The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnK

MPMC

Massively Parallel Monte Carlo (MPMC) is a Monte Carlo method package primarily designed to simulate liquids, molecular interfaces, and functionalized nanoscale materials. It was developed originally

Sampling in order

In statistics, some Monte Carlo methods require independent observations in a sample to be drawn from a one-dimensional distribution in sorted order. In other words, all n order statistics are needed

Fisher–Yates shuffle

The Fisher–Yates shuffle is an algorithm for generating a random permutation of a finite sequence—in plain terms, the algorithm shuffles the sequence. The algorithm effectively puts all the elements i

Inverse transform sampling

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, or the golden rule) is a basic method fo

Multicanonical ensemble

In statistics and physics, multicanonical ensemble (also called multicanonical sampling or flat histogram) is a Markov chain Monte Carlo sampling technique that uses the Metropolis–Hastings algorithm

Tau-leaping

In probability theory, tau-leaping, or τ-leaping, is an approximate method for the simulation of a stochastic system. It is based on the Gillespie algorithm, performing all reactions for an interval o

Transition path sampling

Transition path sampling (TPS) is a Rare Event Sampling method used in computer simulations of rare events: physical or chemical transitions of a system from one stable state to another that occur too

Auxiliary-field Monte Carlo

Auxiliary-field Monte Carlo is a method that allows the calculation, by use of Monte Carlo techniques, of averages of operators in many-body quantum mechanical (Blankenbecler 1981, Ceperley 1977) or c

Multilevel Monte Carlo method

Multilevel Monte Carlo (MLMC) methods in numerical analysis are algorithms for computing expectations that arise in stochastic simulations. Just as Monte Carlo methods, they rely on repeated random sa

Multiple-try Metropolis

Multiple-try Metropolis (MTM) is a sampling method that is a modified form of the Metropolis–Hastings method, first presented by Liu, Liang, and Wong in 2000.It is designed to help the sampling trajec

Preconditioned Crank–Nicolson algorithm

In computational statistics, the preconditioned Crank–Nicolson algorithm (pCN) is a Markov chain Monte Carlo (MCMC) method for obtaining random samples – sequences of random observations – from a targ

Rejection sampling

In numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection metho

Monte Carlo integration

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other

Coupling from the past

Among Markov chain Monte Carlo (MCMC) algorithms, coupling from the past is a method for sampling from the stationary distribution of a Markov chain. Contrary to many MCMC algorithms, coupling from th

James B. Anderson

James Bernhard Anderson (November 16, 1935 – January 14, 2021) was an American chemist and physicist. From 1995 to 2014 he was Evan Pugh Professor of Chemistry and Physics at the Pennsylvania State Un

Reverse Monte Carlo

The Reverse Monte Carlo (RMC) modelling method is a variation of the standard Metropolis–Hastings algorithm to solve an inverse problem whereby a model is adjusted until its parameters have the greate

Resampling (statistics)

In statistics, resampling is the creation of new samples based on one observed sample.Resampling methods are: 1.
* Permutation tests (also re-randomization tests) 2.
* Bootstrapping 3.
* Cross vali

Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as

Metropolis–Hastings algorithm

In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from whi

Replica cluster move

Replica cluster move in condensed matter physics refers to a family of non-local cluster algorithms used to simulate spin glasses. It is an extension of the Swendsen-Wang algorithm in that it generate

Simulated annealing

Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search

Auxiliary particle filter

The auxiliary particle filter is a particle filtering algorithm introduced by Pitt and Shephard in 1999 to improve some deficiencies of the sequential importance resampling (SIR) algorithm when dealin

Marsaglia polar method

The Marsaglia polar method is a pseudo-random number sampling method for generating a pair of independent standard normal random variables. Standard normal random variables are frequently used in comp

Kinetic Monte Carlo

The kinetic Monte Carlo (KMC) method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur

Volumetric path tracing

Volumetric path tracing is a method for rendering images in computer graphics which was first introduced by Lafortune and Willems. This method enhances the rendering of the lighting in a scene by exte

Metropolis light transport

Metropolis light transport (MLT) is a global illumination application of a variant of the Monte Carlo method called the Metropolis–Hastings algorithm to the rendering equation for generating images fr

Glauber dynamics

In statistical physics, Glauber dynamics is a way to simulate the Ising model (a model of magnetism) on a computer. It is a type of Markov Chain Monte Carlo algorithm.

Antithetic variates

In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error in the simulated signal (using Monte Carlo methods) has a one-ov

Monte Carlo tree search

In computer science, Monte Carlo tree search (MCTS) is a heuristic search algorithm for some kinds of decision processes, most notably those employed in software that plays board games. In that contex

Importance sampling

Importance sampling is a Monte Carlo method for evaluating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest.

Monte Carlo molecular modeling

Monte Carlo molecular modelling is the application of Monte Carlo methods to molecular problems. These problems can also be modelled by the molecular dynamics method. The difference is that this appro

Demon algorithm

The demon algorithm is a Monte Carlo method for efficiently sampling members of a microcanonical ensemble with a given energy. An additional degree of freedom, called 'the demon', is added to the syst

Quantum Trajectory Theory

Quantum Trajectory Theory (QTT) is a formulation of quantum mechanics used for simulating open quantum systems, quantum dissipation and single quantum systems. It was developed by Howard Carmichael in

Swendsen–Wang algorithm

The Swendsen–Wang algorithm is the first non-local or cluster algorithm for Monte Carlo simulation for large systems near criticality. It has been introduced by Robert Swendsen and in 1987 at Carnegie

Hamiltonian Monte Carlo

The Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo) is a Markov chain Monte Carlo method for obtaining a sequence of random samples which converge to being distributed accor

Monte Carlo method for photon transport

Modeling photon propagation with Monte Carlo methods is a flexible yet rigorous approach to simulate photon transport. In the method, local rules of photon transport are expressed as probability distr

Biology Monte Carlo method

Biology Monte Carlo methods (BioMOCA) have been developed at the University of Illinois at Urbana-Champaign to simulate ion transport in an electrolyte environment through ion channels or nano-pores e

Probability management

The discipline of probability management communicates and calculates uncertainties as data structures that obey both the laws of arithmetic and probability. The simplest approach is to use vector arra

Particle filter

Particle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to solve filtering problems arising in signal processing and Bayesian statistical inference. The filtering

Ensemble forecasting

Ensemble forecasting is a method used in or within numerical weather prediction. Instead of making a single forecast of the most likely weather, a set (or ensemble) of forecasts is produced. This set

Direct simulation Monte Carlo

Direct simulation Monte Carlo (DSMC) method uses probabilistic Monte Carlo simulation to solve the Boltzmann equation for finite Knudsen number fluid flows. The DSMC method was proposed by Graeme Bird

Event generator

Event generators are software libraries that generate simulated high-energy particle physics events.They randomly generate events as those produced in particle accelerators, collider experiments or th

Dynamic Monte Carlo method

In chemistry, dynamic Monte Carlo (DMC) is a Monte Carlo method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers. It is essentially the sa

Equation of State Calculations by Fast Computing Machines

"Equation of State Calculations by Fast Computing Machines" is a scholarly article published by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller

KBD algorithm

The KBD algorithm is a cluster update algorithm designed for the fully frustrated Ising model in two dimensions, or more generally any two dimensional spin glass with frustrated plaquettes arranged in

Cross-entropy method

The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective.

Iterated filtering

Iterated filtering algorithms are a tool for maximum likelihood inference on partially observed dynamical systems. Stochastic perturbations to the unknown parameters are used to explore the parameter

Pseudo-marginal Metropolis–Hastings algorithm

In computational statistics, the pseudo-marginal Metropolis–Hastings algorithm is a Monte Carlo method to sample from a probability distribution. It is an instance of the popular Metropolis–Hastings a

Quantum jump method

The quantum jump method, also known as the Monte Carlo wave function (MCWF) is a technique in computational physics used for simulating open quantum systems and quantum dissipation. The quantum jump m

Quasi-Monte Carlo method

In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-ran

Monte Carlo methods for electron transport

The Monte Carlo method for electron transport is a semiclassical Monte Carlo (MC) approach of modeling semiconductor transport. Assuming the carrier motion consists of free flights interrupted by scat

Umbrella sampling

Umbrella sampling is a technique in computational physics and chemistry, used to improve sampling of a system (or different systems) where ergodicity is hindered by the form of the system's energy lan

VEGAS algorithm

The VEGAS algorithm, due to G. Peter Lepage, is a method for reducing error in Monte Carlo simulations by using a known or approximate probability distribution function to concentrate the search in th

Stochastic optimization

Stochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization proble

Variance reduction

In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computation

Gillespie algorithm

In probability theory, the Gillespie algorithm (or the Doob-Gillespie algorithm or Stochastic Simulation Algorithm, the SSA) generates a statistically correct trajectory (possible solution) of a stoch

Control variates

The control variates method is a variance reduction technique used in Monte Carlo methods. It exploits information about the errors in estimates of known quantities to reduce the error of an estimate

Wolff algorithm

The Wolff algorithm, named after , is an algorithm for Monte Carlo simulation of the Ising model and Potts model in which the unit to be flipped is not a single spin (as in the heat bath or Metropolis

Mean-field particle methods

Mean-field particle methods are a broad class of interacting type Monte Carlo algorithms for simulating from a sequence of probability distributions satisfying a nonlinear evolution equation. These fl

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