metropolis hastings
时间: 2024-01-07 14:04:37 浏览: 29
Metropolis Hastings is a Markov chain Monte Carlo (MCMC) algorithm used to generate samples from a target probability distribution that is difficult to sample directly. The algorithm is named after its inventors, Nicholas Metropolis and Nicholas Hastings.
The Metropolis Hastings algorithm works by proposing a new state in the Markov chain from the current state, using a proposal distribution. The acceptance probability of the proposed state is then calculated based on the target distribution and the proposal distribution. If the proposed state is accepted, it becomes the new current state in the chain, otherwise the current state remains unchanged.
The algorithm iterates through this process, generating a sequence of states in the Markov chain that eventually converge to the desired target distribution. The convergence of the algorithm depends on the proposal distribution and the acceptance probability function.
The Metropolis Hastings algorithm is widely used in Bayesian statistics, where it is used to generate samples from the posterior distribution of a model. It is also used in physics and other fields where simulation of complex systems is needed.