Shrinkage priors for Bayesian prediction

• 成果类型: Article
• 署名作者: Komaki, Fumiyasu
• 署名单位: University of Tokyo
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000010
• 发表日期: 2006
• 页码: 808-819
• 关键词: second order; estimators; Operators; BOUNDARY

摘要

We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or other vague priors if the model manifold satisfies some differential geometric conditions. Kullback-Leibler divergence from the true distribution to a predictive distribution is adopted as a loss function. Conformal transformations of model manifolds corresponding to vague priors are introduced. We show several examples where shrinkage predictive distributions dominate Bayesian predictive distributions based on vague priors.