| Statistical inference is not merely describing observations but inferring a conclusion from them. At first, we might ask whether a mean effect is zero or not. If we seek differences in specific directions when drawing conclusions, this leads to order restricted inference.;In this dissertation, we present the results of our investigations on hypothesis testing problems with order constraints in microarray studies. The theoretical background of order constrained hypothesis testing and a description of earlier techniques, as well as the mean comparisons problem, will be explained. The main part of the dissertation will focus on normal empirical Bayes models with order constraints, and the study of three distinct topics.;First, we study empirical Bayes models with order constraints in various situations. Empirical Bayes models have been proposed for univariate and multivariate samples, and we summarize the model in all these cases. We also explain some derived statistics in connection with previous empirical Bayes studies. Second, our approach is useful for model comparison. Some classical order restriction studies focus on estimation problems, and different calculations are required for distinct order patterns. The use of empirical Bayes procedures integrates these into a unified model, and leads us a simpler way of comparing models. Third, our empirical Bayes approach can be directly applied to the analysis of gene expression arrays and tiling ChIP-chip data. |
