Bayesian Model-based Approach Research Articles

Identifying Differentially Expressed Genes in Meta-Analysis via Bayesian Model-Based Clustering

A Bayesian model-based clustering approach is proposed for identifying differentially expressed genes in meta-analysis. A Bayesian hierarchical model is used as a scientific tool for combining information from different studies, and a mixture prior is used to separate differentially expressed genes from non-differentially expressed genes. Posterior estimation of the parameters and missing observations are done by using a simple Markov chain Monte Carlo method. From the estimated mixture model, useful measure of significance of a test such as the Bayesian false discovery rate (FDR), the local FDR (Efron et al., 2001), and the integration-driven discovery rate (IDR; Choi et al., 2003) can be easily computed. The model-based approach is also compared with commonly used permutation methods, and it is shown that the model-based approach is superior to the permutation methods when there are excessive under-expressed genes compared to over-expressed genes or vice versa. The proposed method is applied to four publicly available prostate cancer gene expression data sets and simulated data sets.

Reply to Discussion

Scandinavian Journal of StatisticsVolume 31, Issue 2 p. 196-201 Reply to Discussion Donald B. Rubin, Donald B. RubinSearch for more papers by this authorElja Arjas, Elja ArjasSearch for more papers by this author Donald B. Rubin, Donald B. RubinSearch for more papers by this authorElja Arjas, Elja ArjasSearch for more papers by this author First published: 19 May 2004 https://doi.org/10.1111/j.1467-9469.2004.03-200C.x Donald B. Rubin and Elja Arjas E-mail: rubin@stat.harvard.eduE-mail: elja.arjas@rni.helsinki.fi AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume31, Issue2June 2004Pages 196-201 RelatedInformation

A Bayesian approach to computing posterior distribution and quantile functions

Abstract We consider Bayesian techniques for estimating distribution functions and quantile functions from an intractable posterior density function f(·), which are efficient in the sense that relatively few evaluations of f(·) are required. This Bayesian quadrature approach is therefore appropriate when each function evaluation is very expensive. A Gaussian process model is assumed for the prior distribution of f(·), from which we can derive the posterior for f(·) and its integrals. Efficiency is achieved by incorporating prior information about the density function. In particular, we assume f(·) is reasonably well approximated by a normal density. The Bayesian model-based approach also allows us to select optimal evaluation points, and we use this to find an optimal set for estimating univariate distribution functions. If we have the additional information that f(·) integrates to 1, then we show how this information can also be modeled, and can produce more accurate results. The method is demonstrated by integrating a range of density functions with known distribution functions.