A STATISTICAL DIPTYCH - ADMISSIBLE INFERENCES - RECURRENCE OF SYMMETRICAL MARKOV-CHAINS

• 成果类型: Article
• 署名作者: EATON, ML
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348764
• 发表日期: 1992
• 页码: 1147-1179
• 关键词: homogeneous spaces; random-walks

摘要

Given a parametric model and an improper prior distribution, the formal posterior distribution induces decision rules in any decision problem. The results here provide conditions under which this formal Bayes method produces admissible decision rules for all quadratically regular decision problems. The conditions derived are shown to be equivalent to the recurrence of a natural symmetric Markov chain (on the parameter space) generated by the model and the improper prior. The results are also used to give conditions under which formal predictive distributions are admissible decision rules in certain prediction problems.