So, what are Markov chain Monte Carlo (MCMC) methods? The short answer is:MCMC methods are used to approximate the posterior distribution of a parameter of interest by random sampling in a probabilistic space.In this article, I will explain that short answer, without any math.First, some terminology.

A parameter of interest is just some number that summarizes a phenomenon we’re interested in. In general we use statistics to estimate parameters.

For example, if we want to learn about the height of human adults, our parameter of interest might be average height in in inches. A distribution is a mathematical representation of every possible value of our parameter and how likely we are to observe each one.

The most famous example is a bell curve:Courtesy M. W. ToewsIn the Bayesian way of doing statistics, distributions have an additional interpretation. Instead of just representing the values of a parameter and how likely each one is to be the true value, a Bayesian thinks of a distribution as describing our beliefs about a parameter. Read more from…

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