This is the first of a series of posts on Bayesian learning. The learning mechanism which is built into Bayes’ theorem can be used in all sorts of clever ways and has obvious uses in machine learning. Today we’ll build our intuition of how the mechanism works. In the next post, we’ll see how we can use that mechanism to build adaptive regression models.

Bayesian statistics work in the same way as deductive reasoning. Bayes’ theorm *is* a mathematical form of deductive reasoning. It took me a long time to understand this simple but profound idea. Let me say it again: Bayes’ theorm gives us a mathematical way to do deductive reasoning: it allows us to take a piece of evidence, weigh it against our prior suspicions, and arrive at a new set of beliefs. And if we have more evidence, we can do it over and over again.

Let’s do an example. It occured to me that *archaeology* is an excellent illustration of how this works.

## We are archaeologists

We’re excavating the site of a Roman village. Our job is to try and pinpoint what year(s) the village was likely inhabited. In probability terms, we want to work out `p(inhabited)`

for a range of years. As we uncover relics like pottery and coins, we use that evidence to refine our beliefs about when the village was inhabited.

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