Frequency coverage properties of a uniform shrinkage prior distribution

ABSTRACT

A uniform shrinkage prior (USP) distribution on the unknown variance component of a random-effects model is known to produce good frequency properties. The USP has a parameter that determines the shape of its density function, but it has been neglected whether the USP can maintain such good frequency properties regardless of the choice for the shape parameter. We investigate which choice for the shape parameter of the USP produces Bayesian interval estimates of random effects that meet their nominal confidence levels better than several existent choices in the literature. Using univariate and multivariate Gaussian hierarchical models, we show that the USP can achieve its best frequency properties when its shape parameter makes the USP behave similarly to an improper flat prior distribution on the unknown variance component.

KEYWORDS:

• Hierarchical model
• linear mixed model
• variance component
• frequency method checking
• Gibbs sampling
• Markov chain Monte Carlo

Acknowledgments

The author thanks Carl N. Morris for very helpful discussions, Steven R. Finch for proofreading, and the associate editor and referee for their careful reading and insightful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The author acknowledges partial support from the NSF under Grant [DMS 1127914] to the Statistical and Applied Mathematical Sciences Institute.