Q: A magician calls you in and using his magical powers claims to make all coin tosses he does fall a heads. You challenge him, and he tosses the coin once and the coin falls heads. What is the probability that he actually has magical powers? He tosses it again, and it falls heads. What is the probability now that he actually has magical powers?

A: This is classic Bayesian. Assume you have a low belief in this person. Set it as 'p'. He flips the first coin and it lands a heads. This new evidence, which favours the hypothesis must lead us to adjust our belief in our value of 'p'. This may not seem intuitive at first glance, partly because the amount of information is very small (1 toss). But lots of real world problems deal with scarce data (more on that on a later post).

Here is an earlier post describing Bayesian reasoning. So, to cast it in that same framework lets start with our hypothesis.

Hypothesis H = Magical Powers Exist

Evidence E = 1 heads seen on a coin t…

A: This is classic Bayesian. Assume you have a low belief in this person. Set it as 'p'. He flips the first coin and it lands a heads. This new evidence, which favours the hypothesis must lead us to adjust our belief in our value of 'p'. This may not seem intuitive at first glance, partly because the amount of information is very small (1 toss). But lots of real world problems deal with scarce data (more on that on a later post).

Here is an earlier post describing Bayesian reasoning. So, to cast it in that same framework lets start with our hypothesis.

Hypothesis H = Magical Powers Exist

Evidence E = 1 heads seen on a coin t…