Editing Metropolis–Hastings algorithm (section)

== Bayesian Inference ==
{{main article|Bayesian Inference}}
MCMC can be used to draw samples from 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>
where <math>\mathcal{L}</math> is the [[likelihood]], <math>P(\theta)</math> the prior probability density and <math>Q</math> the (conditional) proposal probability.