Bayesian methods are an alternative way of making a statistical inference. We will first look at Bayes' theorem, the fundamental equation from which all Bayesian inference is derived.
A few definitions regarding probability are in order before we begin:
- A,B: These are events that can occur with a certain probability.
- P(A) and P(B): This is the probability of the occurrence of a particular event.
- P(A|B): This is the probability of A happening, given that B has occurred. This is known as a conditional probability.
- P(AB) = P(A and B): This is the probability of A and B occurring together.
We begin with the following basic assumption:
P(AB) = P(B) * P(A|B)
The preceding equation shows the relation of the joint probability of P(AB) to the conditional probability P(A|B) and what is known as the marginal probability, P(B). If...