Estimating cumulative distribution functions from JPS data with empty strata and analyzing high-throughput data via hierarchical Bayesian spatial modeling

This research contains three parts: (1) estimating cumulative distribution functions from JPS data with empty strata; (2) analysis of ChIP-chip data via hierarchical Bayesian spatial modeling; (3) analysis of time course gene expression data.;Judgment Post-Stratification (JPS), similar to ranked set sampling (RSS), is an efficient data collection method by incorporating ranking information. In practice, the sample sizes of JPS data are often small, so empty strata might occur. In the literature, existing methods do not perform well when simply ignoring empty strata. The original isotonized estimator (Ozturk 2007) can handle empty strata automatically through two methods, MinMax and MaxMin. However, blindly using them can result in undesirable results in either tail of the CDF. In this work, we propose modified isotonized estimators to address the empty strata issue and improve estimation efficiency.;ChIP-on-chip is a high throughput technology used to investigate interaction be- tween regulatory proteins and DNA sequences in a genome-wide scope. In molecular psychiatry research, detecting epigenetic changes through the analysis of ChIP-chip data would enable us to gain a better understanding of neurobiological mechanisms and the genetic and environmental factors contributing to major mental disorders. However, analyzing these data is often very challenging due to spatial dependence of the data, with high noise levels and only a few replicates available under each experiment. We propose ANOVA models with spatially varying coefficients, combined with a hierarchical Bayes approach, to explicitly model spatial correlation caused by location-dependent biological effects (i.e., epigenetic changes).;In time course microarray experiments, gene expression levels are measured over multiple time points, allowing us to study dynamic gene regulation. Typically, the sample sizes of time course data are very small, and noise level is high. Furthermore, gene expression levels are often measured at only a few time points. All these make it difficult to model temporal gene expression patterns. In this work, we develop a hierarchical Bayesian approach to model spatial correlation in temporal gene expression patterns among neighboring genes. The proposed method borrows information among different genes and thus can improve the efficiency of the analysis.