Seonglae ChoMetropolis–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
