# Category: Monte Carlo methods

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
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