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Learn Metropolis-Hastings Sampling with R

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}.