文章基本信息

标题：Bayesian Estimation of Correlation Matrices of Longitudinal Data
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作者：Riddhi Pratim Ghosh ; Bani Mallick ; Mohsen Pourahmadi 等
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2021
卷号：16
期号：3
页码：1039-1058
DOI：10.1214/20-BA1237
语种：English
出版社：International Society for Bayesian Analysis
摘要：Estimation of correlation matrices is a challenging problem due to the notorious positive-definiteness constraint and high-dimensionality. Reparameterizing Cholesky factors of correlation matrices in terms of angles or hyperspherical coordinates where the angles vary freely in the range [0,π) has become popular in the last two decades. However, it has not been used in Bayesian estimation of correlation matrices perhaps due to lack of clear statistical relevance and suitable priors for the angles. In this paper, we show for the first time that for longitudinal data these angles are the inverse cosine of the semi-partial correlations (SPCs). This simple connection makes it possible to introduce physically meaningful selection and shrinkage priors on the angles or correlation matrices with emphasis on selection (sparsity) and shrinking towards longitudinal structure. Our method deals effectively with the positive-definiteness constraint in posterior computation. We compare the performance of our Bayesian estimation based on angles with some recent methods based on partial autocorrelations through simulation and apply the method to a data related to clinical trial on smoking.
关键词：angular parameterization; Cholesky decomposition; longitudinal data; selection; shrinkage; structured correlation matrix