Metropolis–Hastings algorithm: Difference between revisions

Revision as of 06:13, 16 June 2023

Revision as of 06:14, 16 June 2023

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{{main article|Bayesian Inference}}

[[File:Flowchart-of-Metropolis-Hastings-M-H-algorithm-for-the-parameter-estimation-using-the.png|thumb|Flowchart of Metropolis-Hastings (M-H) algorithm for the parameter estimation using the Markov Chain Monte Carlo (MCMC) approach.]]

MCMC can be used to estimatedraw optimalsamples parametersfrom the [[posterior distribution]] of a statistical model.

The acceptance probability is given by:

<math>P_{acc}(\theta_i \to \theta^*)=\min\left(1, \frac{\mathcal{L}(y|\theta^*)P(\theta^*)}{\mathcal{L}(y|\theta_i)P(\theta_i)}\frac{Q(\theta_i|\theta^*)}{Q(\theta^*|\theta_i)}\right),</math>