Proteomics is the science that deals with high-throughput analysis of proteins. The study of proteins relies on efficient protein separation technique. 2D PAGE is a powerful technique for separating complex mixtures of proteins, where thousands of proteins are separated and measured simultaneously. The analysis of 2D PAGE images needs efficient methods able to cope with large-scale dataset. Empirical Bayes methods have been shown to be very efficient at combining information across dimensions of high-dimensional data.

In the first part of this dissertation, the construction of empirical Bayes confidence intervals under different model assumptions is studied. Numerical simulations are conducted to demonstrate the satisfactory performance of the proposed methods. In the second part, a new comprehensive procedure for statistical analysis of 2D PAGE images is proposed, including protein quantification, normalization and statistical analysis. It reduces the dimension of the data. It also bypasses the current bottleneck in the analysis of 2D PAGE images in that it does not require spot matching. A strategy for multiple hypothesis testing based on multivariate analysis combined with empirical Bayes methods is formulated and applied to the differential analysis of 2D PAGE images. The new methodologies are implemented in a custom software package.