Math459:
Bayesian Statistics

Links
What is Bayesian
statistics and why everything else is wrong?
Why isn't everyone a Bayesian? Bayes in the newsThe Mathematics of Changing Your Mind You Might Already Know This ... A Bayesian Take on Julian Assange 
Bayesian statistics has a fundamentally different view to statistical
inference from the classic (frequentist) inference.
Knowledge of the concerned problem prior to data collection is represented by
a probability distribution (prior distribution), and after the data are collected,
this distribution is updated using Bayes' theorem, and then called posterior
distribution. All Bayesian inference is then based on this posterior
distribution. Philosophically, this process is very similar to the scientific
discovery process. Advantages of Bayesian statistics include, the inference is
conditional on the given data; prior knowledge can be integrated into the
analysis using prior distributions; and modeling complex systems can be done
easily using hierarchical models. Disadvantages include, different priors
lead to different inference; and computation is often intensive. After this class, students will master the basic principle of
Bayesian inference and its applications in different models, such as prior
specification, Markov chain Monte Carlo, Gibbs Sampling, Bayes factor,
empirical Bayes, analysis of hierarchical models, etc. We will use R and WinBUGS for data
analysis and have some computer lab sessions in which students will gain
handon experiences on real data analysis. 
