Metropolis Algorithm

Created

Created

2022 Apr 3 15:50

Editor

Editor

Seonglae Cho

Creator

Creator

Seonglae Cho

Edited

Edited

2025 Apr 29 1:52

Refs

Refs

Rejection Sampling

Metropolis–Hastings algorithm (MH algorithm)

A flagship MCMC algorithm that uses proposal distribution with Monte Carlo sampling and filters based on Acceptance Criteria.

MH makes local changes to a current state. We use the proposal and the transition to define an ”acceptance ratio” :

Symmetric MH

Note that in the (popular) choice of Gaussian perturbations,

then the proposal is ”symmetric”

sample a value from proposal

if , then move to with certainity

otherwise, move to with probability

Metropolis-Hastings algorithm - Wikipedia

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 which direct sampling is difficult. This sequence can be used to approximate the distribution (e.g. to generate a histogram) or to compute an integral (e.g.

https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm

Metropolis-Hastings algorithm - Wikipedia

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