What is Bayes Theorem?¶
Bayes theorem is what allows us to go from a sampling (or likelihood) distribution and a prior distribution to a posterior distribution.
What is a Sampling Distribution?¶
A sampling distribution is the probability of seeing our data (X) given our parameters ($\theta$). This is written as $p(X|\theta)$.
For example, we might have data on 1,000 coin flips. Where 1 indicates a head. This can be represented in python as