Math459: Bayesian Statistics


What is Bayesian statistics and why everything else is wrong?


Why isn't everyone a Bayesian?

Bayes in the news


The Mathematics of Changing Your Mind


You Might Already Know This ...


Chances Are ...


A Bayesian Take on Julian Assange


How do children learn so quickly?


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 hand-on experiences on real data analysis.


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