Bayesian Statistics: Handouts

HANDOUT1: Probability, Conditional Probability and Bayes Formula. This handout is mainly refresher in elementary probability, conditioning and independence. Total Probability and Bayes Formula (in terms of events) are covered with plenty of examples.

HANDOUT2: Likelihood Principle. Conditional Point of View.

HANDOUT3: Likelihood, prior, posterior, marginal. Notation and a couple of examples. Unfinished handout -- much to be added.

HANDOUT4: Basic Decision Theoretic Concepts.

HANDOUT5: Priors. Conjugate, Jeffreys.

HANDOUT6: Priors. Normal-Inverse Gamma, MaxEnt, Multivariate.

HANDOUT7: Bayes Estimation and Credible Sets. Testing Statistical Hypotheses in Bayesian Fashion. Examples.

HANDOUT8: Hierarchical Bayesian Modeling. Empirical Bayes. ML II Method. Preliminary Version.

HANDOUT9: Bayesian Computation. Numerical Algorithms and Monte Carlo Methods. Importance Sampling and ARM (accept/reject method).

HANDOUT10: MCMC: Metropolis and family of algorithms. Gibbs Sampler. Just a first version...

HANDOUT11: MCMC: Various Models and Sampling Related Stuff (slice sampling, Rao-Blackwellization).

HANDOUT12: EM Algorithm. Basics. Application in MAP rules. Mixtures. EM and MCMC treatments of Mixture problems.

HANDOUT13: A sketchy and incomplete handout on Sequential Monte Carlo. Updates to follow.

HANDOUT14: BUGS Intro. Just getting started.

HANDOUT15: Yet another half baked handout. This one is on Bayesian Model Selection. Model Averaging will be addedd.

HANDOUT16: Gibbs Distributions and Markov Random Fields, Genuine Gibbs, Ising Model, Image Analysis.

HANDOUT17: Bayes Graphical Models. Much to be added. Our Matt Wiggins graciously made figures.

HANDOUT18: (Not Posted Yet) Bayes Discriminators. TALK at ISBA 2004 at Vina del Mar in Chile, that has some relevance to the topic.

HANDOUT19: (Not Posted Yet) Bayesian Analysis in Time Series. Long Range Dependence, Self-similarity, Fractality and Multifractality and Chaos.

HANDOUT20: Basics of Wavelet Transforms.

HANDOUT21: Bayes Wavelet Shrinkage. Overview of Some Methods.

HANDOUT0: Some continuous distributions and their properties. Discrete and multivariate distributions will be added.

HANDOUT00: Mathematical and Probability Prerequisites. Review. Planned.

Last Updated: August 15, 2004.