A correlation-shrinkage prior for Bayesian prediction of the two-dimensional Wishart model. (1st February 2022)

• Record Type: Journal Article
• Authors: Sei, T; Komaki, F
• Is Part Of: Biometrika. Volume 109:Number 4(2022)
• Page Start: 1173
• Page End: 1180
• Publication Date: 2022-02-01
• Subjects: Decision theory -- Gauss hypergeometric function -- Minimaxity -- Right invariant prior -- Scale invariance -- Superharmonic prior; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asac006
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: A Bayesian prediction problem for the two-dimensional Wishart model is investigated within the framework of decision theory. The loss function is the Kullback–Leibler divergence. We construct a scale-invariant and permutation-invariant prior distribution that shrinks the correlation coefficient. The prior is the geometric mean of the right invariant prior with respect to permutation of the indices, and is characterized by a uniform distribution for Fisher's $z$ -transformation of the correlation coefficient. The Bayesian predictive density based on the prior is shown to be minimax.