Deriving the Posterior Distribution

In the preceding chapters, we discussed how we can assign a prior distribution for our parameters and how to choose a likelihood function that captures the information content of our data. So all that is left is to apply Bayes’ Theorem (Eq. ( 2.2 )) to derive our desired posterior distribution. Note that when talking about the posterior, we use the phrase ‘deriving the’ distribution rather than ‘assigning a’ distribution. That is because Bayes’ Theorem tells us exactly what the posterior distribution should be once we have defined our prior and likelihood.