Discovered in 1933. Popularized in 2010.

Simple schoolbook A/B testing example: pick which of 2 websites to show a visitor, using a coin flip… in other words, draw from a Bernoulli distribution to decide which site to show.

Thompson uses a beta distribution to weight how often to show the one or the other version of the website to customers. The beta dist has 2 parameters, α and β. Here these parameters represent prior successes and fails (wins and losses), by count. We must of course define what win and fail mean, e.g. when visitor clicks the buy button it's a win, else a fail.

Going about things with Thompson sampling you win a lot of efficiency, your company doesn't lose much revenue while you're running the A/B experiment, since the one shown to work better is quickly shown more often.

Bayesian methods

The problem with tracking tiny probabilities like 0.0001%, aside from the rather larger chance of human error, is that no-one can feel a probability that small. If you must talk about such numbers anyway, remember: though you can write a symbolic description of this probability, a feeling that small doesn't exist, doesn't fire enough neurons or release enough neurotransmitters, so it's not actually an object worth keeping track of consciously (you'd lend it overmuch respect), any more than any Flying Spaghetti Monster proposition.

So when the math gives you a number this small, discount the hypothesis entirely. The only cause for doubt is the question of whether you did the math correctly. The thought "ok it's tiny, but not zero, so there's still a chance, right?" is one you should be wary to ever find yourself generating.

Plus if you Visualize probability as shades of grey, the human-perceptual difference between the black of 0.0001% and the black of 0% is… indistinguishable. Why then keep any track of 0.0001%?

Shades of grey. There are shades so bright as to be essentially white, and shades so dark that for all intents and purposes, they're black.

arithmetic mean:

x1 + x2 + x3 __ 3

geometric mean

x1 * x2 * x3 __ 3

Used when the involved quantities have different scales.