# Markov Chain Monte Carlo

## Hierarchical Linear Model

Linear regression probably is the most familiar technique in data analysis, but its application is often hamstrung by model assumptions. For instance, if the data has a hierarchical structure, quite often the assumptions of linear regression are feasible only at local levels. We will investigate an extension of the linear model to bi-level hierarchies.

## Bayesian Classification with Gaussian Process

Despite prowess of the support vector machine, it is not specifically designed to extract features relevant to the prediction. For example, in network intrusion detection, we need to learn relevant network statistics for the network defense. In consumer credit rating, we would like to determine relevant financial records for the credit score. As for medical genetics research, we aim to identify genes relevant to the illness.

## Bayesian Inference Using OpenBUGS

In our previous statistics tutorials, we have treated population parameters as fixed values, and provided point estimates and confidence intervals for them. An alternative approach is the Bayesian statistics. It treats population parameters as random variables. Probability becomes a measure of our belief in possible outcomes. With new tools like OpenBUGS, tackling new problems requires building new models, instead of creating yet another R command.