Abstract not found

We consider the choice of an optimal sample size for multiple comparison problems. The motivating application is the choice of the number of microarray experiments to be carried out when learning about dierential gene expression. However, the approach is valid in any application that involves multiple comparison in a large number of hypothesis tests.

DNA microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease. The high throughput nature of these arrays, where differential expression for thousands of genes can be measured simultaneously, creates an enormous wealth of information, but also poses a challenge for data analysis because of the large multiple testing problem involved. The solution has generally been to focus on optimizing false-discovery rates while sacri � cing power. The drawback of this approach is that more subtle expression differences will be missed that might give investigators more insight into the genetic environment necessary for a disease process to take hold. We introduce a new method for detecting differentially expressed genes based on a high-dimensional model selection technique, Bayesian ANOVA for microarrays (BAM), which strikes a balance between false rejections and false nonrejections. The basis of the new approach involves a weighted average of generalized ridge regression estimates that provides the bene � ts of using shrinkage estimation combined with model averaging. A simple graphical tool based on the amount of shrinkage is developed to visualize the trade-off between low false-discovery rates and � nding more genes. Simulations are used to illustrate BAM’s performance, and the method is applied to a large database of colon cancer gene expression data. Our working hypothesis in the colon cancer analysis is that large differential expressions may not be the only ones contributing to metastasis—in fact, moderate changes in expression of genes may be involved in modifying the genetic environment to a suf � cient extent for metastasis to occur. A functional biological analysis of gene effects found by BAM, but not other false-discovery-based approaches, lends support to this hypothesis.

We consider the problem of identifying differentially expressed genes under different conditions using cDNA microarrays. Standard statistical methods cannot be used because typically there are thousands of genes and few replicates. Because of the many steps involved in the experimental process, from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outlying data value could occur because of scratches or dust on the surface, imperfections in the glass, or imperfections in the array production. We develop a robust Bayesian hierarchical model for testing for differential expression. Outliers are modeled explicitly using a t-distribution. The model includes an exchangeable prior for the variances which allow different variances for the genes but still shrink extreme empirical variances. Our model can be used for testing for differentially expressed genes among multiple samples, and can distinguish between the different possible patterns of differential expression when there are three or more samples. Parameter estimation is carried out using a novel version of Markov Chain Monte Carlo that is appropriate when the model puts mass on subspaces of the full parameter space. The method is illustrated using two publicly available

1 Summary. In epidemiologic studies, there is often interest in assessing the relationship between polymorphisms in functionally-related genes and a health outcome. For each candi-date gene, single nucleotide polymorphism (SNP) data are collected at a number of locations, resulting in a large number of possible genotypes. Because instabilities can result in analy-ses that include all the SNPs, dimensionality is typically reduced by conducting single SNP analyses or attempting to identify haplotypes. This article proposes an alternative Bayesian approach for reducing dimensionality. A multi-level Dirichlet process prior is used for the distribution of the SNP-specific regression coefficients within genes, incorporating a variable selection-type mixture structure in the base measure to allow SNPs with no effect. This structure allows simultaneous selection of important SNPs and clustering of SNPs having similar impact on the health outcome. The methods are illustrated using data from a study

We present new techniques for the application of a Bayesian network learning framework to the problem of classifying gene expression data. The focus on classification permits us to develop techniques that address in several ways the complexities of learning Bayesian nets. Our classification model reduces the Bayesian network learning problem to the problem of learning multiple subnetworks, each consisting of a class label node and its set of parent genes. We argue that this classification model is more appropriate for the gene expression domain than are other structurally similar Bayesian network classification models, such as Naive Bayes and Tree Augmented Naive Bayes (TAN), because our model is consistent with prior domain experience suggesting that a relatively small number of genes, taken in different combinations, is required to predict most clinical classes of interest. Within this framework, we consider two different approaches to identifying parent sets which are supported by the gene expression observations and any other currently available evidence. One approach employs a simple greedy algorithm to search the universe of all genes; the second approach develops and applies a gene selection algorithm whose results are incorporated as a prior to enable an exhaustive search for parent sets over a restricted universe of genes. Two other significant contributions are the construction of classifiers from multiple, competing Bayesian network hypotheses and algorithmic methods for normalizing and binning gene expression data in the

This paper considers several Bayesian classification methods for the analysis of the glioma cancer with microarray data based on reproducing kernel Hilbert space under the multiclass setup. We consider the multinomial logit likelihood as well as the likelihood related to the multiclass Support Vector Machine (SVM) model. It is shown that our proposed Bayesian classification models with multiple shrinkage parameters can produce more accurate classification scheme for the glioma cancer compared to several existing classical methods. We have also proposed a Bayesian variable selection scheme for selecting the differentially expressed genes integrated with our model. This integrated approach improves classifier design by yielding simultaneous gene selection. AMS (2000) subject classification. Primary 62G08, 62H30, 68T05, 68T10. Keywords and phrases. Gibbs sampling, Markov chain Monte Carlo, Metropolis-Hastings algorithm, microarrays, reproducing kernel Hilbert space, shrinkage parameters, support vector machines. 1

Bayesian analysis of gene expression levels: statistical quantification of relative mRNA level across multiple strains or treatments