Sublime

The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new.

Bayes’ theorem is the same idea, but taken a bit further. In natural language, it means: the probability of event A, given event B, equals the probability of B given A, times the probability of A on its own, divided by the probability of B on its own.

And for any power-law distribution, Bayes’s Rule indicates that the appropriate prediction strategy is a Multiplicative Rule: multiply the quantity observed so far by some constant factor.

this is usually stated as: the probability of your hypothesis (‘the die is weighted’) given your evidence (the rolls you’ve seen) is proportional to the probability of your evidence given your hypothesis (the odds you’d see those rolls if the die were weighted) times the probability of your hypothesis (how likely is the die to be weighted to begin