Week 3
Fundamental Distributions
Beta
Binomial
Exponential
Gamma
Possion
Conjugate Prior
The idea of conjugate prior is that we choose a prior distribution such that, after observing data and applying Bayes’ theorem, the posterior distribution belongs to the same family as the prior.
That is, if and have the same distributional form, then the prior is called a conjugate prior for the likelihood model.
This is useful because it makes Bayesian updating analytically tractable. Instead of performing difficult integration or numerical approximation, we can often derive the posterior parameters in closed form.
Problem 1 Conjugate Prior