時 間：114年9月30日（星期二下午14:10~15:00）
地 點：管理學院新大樓M242
主講人：王紹宣 教授 (中央大學 統計研究所)
講 題：Bayesian Sparse Kronecker product decomposition
Abstract
The Sparse Kronecker Product Decomposition (SKPD) for tensor data was introduced by Sanyou Wu and Long Feng (2023). This method represents the first frequentist framework designed for signal region detection in high-resolution, high-order image regression problems. Their work demonstrated the strong performance of SKPD in various applications.
In this presentation, we will introduce a Bayesian version of SKPD, referred to as Bayesian SKPD. From a Bayesian perspective, we apply a three-parameter beta-normal prior family to the parameters of interest. Additionally, we address tensor regression data with mixed-type responses using Polya-Gamma augmentation. This approach allows us to give credible region detection through direct Gibbs sampling. The theoretical results will be presented, and we will demonstrate the effectiveness of Bayesian SKPD using real brain imaging data from the OASIS.