Minimax predictive density for sparse count data

Yano, Keiji; Kaneko, Ryoya; Komaki, Fumiyasu

doi:10.3150/20-bej1271

Cited by 4 publications

(1 citation statement)

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“…While extensively studied for Gaussian data, the global-local shrinkage priors have not been fully developed for count data, although Poisson likelihood models with hierarchical structure are widely used in applications such as disease mapping (see, for example, Wakefield 2006 andLawson 2013). The theory related to the Poisson likelihoods has been well developed, but not necessarily from the viewpoint of global-local shrinkage (e.g., Brown et al 2013 andYano et al 2019). The standard Bayesian models for count data is of Poisson-gamma type; the gamma prior for the Poisson rate shows the similarity to the global-local shrinkage prior if one assumes further hierarchical prior on the gamma scale parameters.…”

Section: Introductionmentioning

confidence: 99%

On Global-local Shrinkage Priors for Count Data

Hamura

Irie

2019

Preprint

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Global-local shrinkage prior has been recognized as useful class of priors which can strongly shrink small signals towards prior means while keeping large signals unshrunk. Although such priors have been extensively discussed under Gaussian responses, we intensively encounter count responses in practice in which the previous knowledge of global-local shrinkage priors cannot be directly imported. In this paper, we discuss global-local shrinkage priors for analyzing sequence of counts. We provide sufficient conditions under which the posterior mean keeps the observation as it is for very large signals, known as tail robustness property. Then, we propose tractable priors to meet the derived conditions approximately or exactly and develop an efficient posterior computation algorithm for Bayesian inference. The proposed methods are free from tuning parameters, that is, all the hyperparameters are automatically estimated based on the data. We demonstrate the proposed methods through simulation and an application to a real dataset.

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Section: Introductionmentioning

confidence: 99%