4. Inference and PDFs

In this chapter we put on the table the basic ingredients for Bayesian inference. The subsections are:

• Statements: Notation for probability statements

• Manipulating probabilities: Bayesian rules of probability as principles of logic

• Probability density functions. Extension of the Bayesian rules of probability to continuous probability density functions.

• Expectation values and moments: pointers to further insight on Bayes’ theorem

• Review of Bayes’ theorem. Further details on Bayes’ theorem.

• Data, models, and predictions. Introduction to statistical models, posterior predictive distributions, and Bayesian parameter estimation.

• *Aside: Bayesian epistemology. Philosophical remarks on the interpretation of probabilities.