An Introduction to Bayesian Hypothesis Testing for ANOVA Designs
A/Prof. Min Wang
Department of Mathematics and Statistics, Texas Tech University, USA

We explore Bayesian approaches for the hypothesis testing problem in multiway ANOVA models. We first specialize the result in a two-sample scenario as an intermediate step toward developing the Bayes factors for ANOVA designs. Given that the design matrix is not necessarily of full rank, we adopt the sum-to-zero constraint for uniqueness and employ the singular value decomposition (SVD) method to reparameterize the model to get rid of the additional constraint. We then derive the Bayes factors under a class of Zellner's g-priors. We examine asymptotic properties of the proposed procedures with a diverging dimensionality. Our results indicate that commonly used hyper-priors yield inconsistent Bayes factors due to the presence of an inconsistency region around the null model. We propose a new class of hyper-priors to avoid this inconsistency problem. Simulation studies on two-way ANOVA models are conducted to compare the performance of the proposed priors with that of some existing ones in the literature.

About the Speaker

汪敏(Min Wang), 美国德克萨斯理工大学 (Texas Tech University)数学统计系副教授。2010年5月于美国克莱姆森大学(Clemson University) 获得统计硕士学位; 2013年5月于克莱姆森大学大学获得统计博士学位。2013年8月- 2017年12月在美国密歇根理工大学数学科学系工作和在2017年8月破格提前提升为副教授并获得终身任期教授资格; 随后, 他在2018年1月-至今在美国德克萨斯理工大学从事教学科研工作。近年来, 先后参与和主持了美国自然科学基金委(NSF), 密歇根交通部, 以及美国卫生院(NIH)的研究课题。在各类同行评议的国际权威期刊上发表了研究文章40余篇。研究方向: 贝叶斯统计; 计算统计; 统计推断; 质量和可靠性工程研究; 高维数据分析和统计应用。

2018-07-16 4:00 PM
Room: A203 Meeting Room
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