Bayesian Hierarchical Model for Identifying Changes in Gene Expression from Microarray Experiments
Recent developments in microarrays technology enable researchers to study simultaneously the expression of thousands of genes from one cell line or tissue sample. This new technology is often used to assess changes in mRNA expression upon a specified transfection for a cell line in order to identify target genes. For such experiments, the range of differential expression is moderate, and teasing out the modified genes is challenging and calls for detailed modeling. The aim of this paper is to propose a methodological framework for studies that investigate differential gene expression through microarrays technology that is based on a fully Bayesian mixture approach (Richardson and Green, 1997). A case study that investigated those genes that were differentially expressed in two cell lines (normal and modified by a gene transfection) is provided to illustrate the performance and usefulness of this approach.
It is the purpose of this paper to introduce a novel estimator for the extremal index of an instantaneous function {f(Xn)}n of a regenerative Harris Markov chain X, based on the renewal properties of the latter. The estimate proposed may be viewed as a "regenerative version" of the runs estimator, insofar as it measures the clustering tendency of high threshold exceedances within regeneration cycles. Strong consistency of this estimator is established under mild stochastic stability assumptions and a simulation result is displayed in the case when the underlying chain is the waiting process related to a simple M/M/1 queue.