Bayesian probability

Bayesian probability is a quirky branch of statistics which stretches the limits of reason but also delivers some very common sense conclusions.

First a simple explanation of the difference between the classic (frequentist) and Bayesian probability. Let’s imagine that you have lost a sock. Let’s further assume you are equally likely to have lost it in the bedroom or the bathroom. Subsequent to this painful loss you have carried an extensive search in the bedroom and also had a cursory look in the bathroom but no sock was found. What is the probability split of the sock residing in the bedroom vs the bathroom?

In the frequentist statistics it is 50/50. The sock is equally likely to have been lost in the bedroom or the bathroom. It cannot have moved from one room to the other since so the original probabilities still hold. Your subsequent search is irrelevant.

The Bayesian approach is different. True, the sock is equally likely to have originally been lost in either of the rooms. However  you have since had more chance to locate it in the bedroom than in the bathroom. The fact you have spent more time unsuccessfully looking for it in the bedroom makes it more likely the sock is hiding in the bathroom.

I do not know about you but I am finding the Bayesian proposition stunning. It claims, in simple terms, that the original (prior) probabilities can be altered by the subsequent (posterior) events. Technically we are not talking about the same probability. Frequentists look at the original event i.e. you losing the sock. Bayesians assess the probability of you finding the sock after the first, unsuccessful, search. But, one may ask, how can we find the sock where it has not been lost so, logically, should not both probabilities be the same?

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