## Posts List

In this blog post I hope to introduce you to the powerful and simple Metropolis-Hastings algorithm. This is a common algorithm for generating samples from a complicated distribution using Markov chain Monte Carlo, or MCMC. By way of motivation, remember that Bayes’ theorem says that given a prior $$\pi(\theta)$$ and a likelihood that depends on the data, $$f(\theta | x)$$, we can calculate \[ \pi(\theta | x) = \frac{f(\theta | x) \pi(\theta)}{\int f(\theta | x) \pi(\theta) \; \mathrm{d}\theta}.