統計学輪講（第12回） 日時 2012年07月10日(火) 15時40分～16時30分 場所 経済学部新棟３階第３教室 講演者 Mohammad Manir Hossain Mollah (農D3) 演題 Robust Bayesian inference and model diagnosis of microarray data by β-likelihood 概要 In high-throughput analysis, it is generally difficult to scrutinize the irregular patterns of expression that are not expected by the statistical model gene by gene. In this talk, we propose a β-empirical Bayes (β-EB) approach based on a β-likelihood measure. β-likelihood approach is regarded as a weighted likelihood procedure. The weight of a gene t is described as a power function of its likelihood, fβ(yt|θ). By putting low weights on the data that have small likelihoods with unexpected expression patterns, the inference becomes robust. Because of its high-dimensionality, the distribution of the weights can be used to detect outliers and diagnose the model statistically. From the simulation results, we observe that the proposed method significantly improves the performance in a comparison of the others in presence of outliers; otherwise, it keeps almost equal performance. An application of the proposed method to the head and neck cancer data detect several biologically important DE genes, whose expressions are confirmed to be unstable. They were not detected by standard EB approach. Analysis of the data from patients of two types of lung cancer identiﬁed mis-specification of the model. The β-likelihood based eQTL analysis implied that the classical approach may under estimate the number of target genes of master transcription factors largely.