What is metropolis hastings?

Metropolis-Hastings is a commonly used Markov Chain Monte Carlo (MCMC) algorithm used for simulating draws from a target distribution. The algorithm is primarily used in Bayesian statistics and machine learning for sampling from complex probability distributions, where it is difficult or impossible to directly sample from.

The Metropolis-Hastings algorithm works by constructing a Markov chain that iterates through a sequence of proposed candidate samples. At each iteration, a candidate sample is generated based on a proposal distribution and then accepted or rejected based on an acceptance probability, which is calculated using the target distribution of interest.

The algorithm guarantees convergence to the target distribution as the number of iterations goes to infinity. However, the efficiency and speed of convergence of the algorithm can be influenced by the choice of proposal distribution and the tuning of its parameters.

Metropolis-Hastings is a widely used and versatile MCMC algorithm that has been successfully applied to a wide range of statistical problems, including Bayesian inference, parameter estimation, and model fitting.