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.

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。