Li: High-dimensional feature selection using hierarchical Bayesian logistic regression with heavy-tailed priors | Rao: Best predictive estimation for linear mixed models with applications to small area estimation

Date: 2012-04-13

Time: 14:00-16:30

Location: MAASS 217

Abstract:

Li: The problem of selecting the most useful features from a great many (eg, thousands) of candidates arises in many areas of modern sciences. An interesting problem from genomic research is that, from thousands of genes that are active (expressed) in certain tissue cells, we want to ﬁnd the genes that can be used to separate tissues of diﬀerent classes (eg. cancer and normal). In this paper, we report a Bayesian logistic regression method based on heavytailed priors with moderately small degree freedom (such as 1) and small scale (such as 0.01), and using Gibbs sampling to do the computation. We show that it can distinctively separate a couple of useful features from a large number of useless ones, and discriminate many redundant correlated features. We also show that this method is very stable to the choice of scale. We apply our method to a microarray data set related to prostate cancer, and identify only 3 genes out of 6033 candidates that can separate cancer and normal tissues very well in leave-one-out cross-validation.

Rao: We derive the best predictive estimator (BPE) of the fixed parameters for a linear mixed model. This leads to a new prediction procedure called observed best prediction (OBP), which is different from the empirical best linear unbiased prediction (EBLUP). We show that BPE is more reasonable than the traditional estimators derived from estimation considerations, such as maximum likelihood (ML) and restricted maximum likelihood (REML), if the main interest is the prediction of the mixed effect. We show how the OBP can significantly outperform the EBLUP in terms of mean squared prediction error (MSPE) if the underlying model is misspecified. On the other hand, when the underlying model is correctly specified, the overall predictive performance of the OBP can be very similar to the EBLUP. The well known Fay-Herriot small area model is used as an illustration of the methodology. In addition, simulations and analysis of a data set on graft failure rates from kidney transplant operations will be used to show empirical performance. This is joint work with Jiming Jiang of UC-Davis and Thuan Nguyen of Oregon Health and Science University.

Speaker

Longhai Li is an Assistant Professor of Statistics at the University of Saskatchewan

Sunil Rao is a Professor and Director of the Division of Biostatistics at the Department of Epidemiology and Public Health, University of Miami