Bayes In the Real World: The Metropolis-Hastings Algorithm

Last time, we talked about Bayesian statistics as a powerful framework to learn from data and make decisions in an uncertain world. I ended on a bit of downer: unfortunately, the math behind Bayesian statistics is only tractable in a small set of problems. In order to use Bayesian inference in the real world, we're going to have to find ways of approximating the correct answer when finding it exactly is impossible. The existence of algorithms to do this is why Bayesian statistics is in a renaissance: before ten or fifteen years ago, finding an intractable integral was simply a dead end. Now, it's possible to press on, unlocking the power of Bayesian inference in far more applications.

The Metropolis-Hastings algorithm is the first step on the road to the cutting edge of today, and its concepts underpin almost every approach that came after it. So what is this seminal algorithm, and what problem does it solve? I'll begin by describing it abstractly, without reference to Bayes, and then next time I'll apply it to a Bayesian inference problem.

Bayes In the Real World: The Metropolis-Hastings Algorithm

Last time, we talked about Bayesian statistics as a powerful framework to learn from data and make decisions in an uncertain world. I ended on a bit of downer: unfortunately, the math behind Bayesian statistics is only tractable in a small set of problems. In order to use Bayesian inference in the real world, we're going to have to find ways of approximating the correct answer when finding it exactly is impossible. The existence of algorithms to do this is why Bayesian statistics is in a renaissance: before ten or fifteen years ago, finding an intractable integral was simply a dead end. Now, it's possible to press on, unlocking the power of Bayesian inference in far more applications.

The Metropolis-Hastings algorithm is the first step on the road to the cutting edge of today, and its concepts underpin almost every approach that came after it. So what is this seminal algorithm, and what problem does it solve? I'll begin by describing it abstractly, without reference to Bayes, and then next time I'll apply it to a Bayesian inference problem.