Basic Stucture

The Basis for this course is to develop an understanding of Bayesian principles and methodologies. We will develop the basis for subjective probability and illustrate why this is a necessary construct in many applications where classical notions of probability are degenerate. Computational examples will augment much of the material.

Probability does not exist. -De Finetti

Topics to be discussed in this course follow as:

• Philosophy: What is probability?
• Fisher vs Neyman vs Jeffreys.
• The Likelihood Principle

• Basic Bayesian constructions: Likelihoods, priors and posteriors.

• Exponential families and conjugate priors.
• Asymptotics, Bayesian t-tests, mixture models, hierarchical modeling, etc...

Many examples will be centered around the above methodologies. You will get a lot of practice manipulating posterior distributions.

We will next move on to:

• Bayesian sequential updating.
• More on priors: Jeffreys, Reference, Objective, Subjective, etc...
• Simulation procedures: Gibbs, Metropolis, etc...
• Model Selection: Theory and Computational Approaches