Lecture 1

The concept of probability in Bayesian Statistics. The Sum and Product Rules.

Bayes’s Theorem. Example: Least Squares Minimization - Chi2.

The Coin Example (the effect of sample size and varying priors).

Lecture 2

Nuisance parameters and Marginalization

Example: An Astrophysical application of the Coin Example

Coordinate Transformations. Example: Derivation of the ‘Sum in Quadrature’ rule.

Parallax example (negative measurements of the parallax, effect of positive definite prior for the distance).

Lecture 3

Probability distributions: example applications. Fitting a density model to data (Poisson), the IMF example (Pareto distribution).

Lecture 4

Many parameter problems: Importance sampling and Markov Chain Monte Carlo. A familiar example using MCMC (the astrophysical coin example). Topics: ABC - Approximate Bayesian Computation. Examples.