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When I give talks about probabilistic programming and Bayesian statistics, I usually gloss over the details of how inference is actually performed, treating it as a black box essentially. The beauty of probabilistic programming is that you actually don’t have to understand how the inference works in order to build models, but it certainly helps.

When I presented a new Bayesian model to Quantopian’s CEO, Fawce, who wasn’t trained in Bayesian stats but is eager to understand it, he started to ask about the part I usually gloss over: “Thomas, how does the inference actually work? How do we get these magical samples from the posterior?”.

Now I could have said: “Well that’s easy, MCMC generates samples from the posterior distribution by constructing a reversible Markov-chain that has as its equilibrium distribution the target posterior distribution. Questions?”.

That statement is correct, but is it useful? My pet peeve with how math and stats are taught is that no one ever tells you about the intuition behind the concepts (which is usually quite simple) but only hands you some scary math. This is certainly the way I was taught and I had to spend countless hours banging my head against the wall until that euraka moment came about. Usually things weren’t as scary or seemingly complex once I deciphered what it meant.

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