Bayesian Analysis of a change-point Poisson Process

布瓦松過程具轉折點之貝氏分析

林億雄(Yi-Hsiung Lin) ； 任眉眉(Mei-Mei Zen)

《致遠管理學院學報》 2_2期 (2007/09) Pp. 1-15

https://doi.org/10.6595/BDCM.2007.2(2).1

摘要

對於具有轉折點的布瓦松過程，其前驗分布一般均考量均勻分布，但考量單峰分布則較為符合實際情形，同時可顯出轉折點的特性。本文首先考量一些常用的單峰前驗分布，其次使用第二型最大概似估計藉以求得經驗貝氏估計量。關於如何決定適當的前驗分布，本文使用貝氏因子法則。其經驗貝氏估計量的計算則使用蒙地卡羅積分方法，此統計方法用於分析一組煤礦災變資料。根據研究結果，貝他前驗分布在轉折點分析上有較佳表現，並能呼應配置單峰前驗分布的合理性。

關鍵字

貝氏因子 ； 煤礦災變資料 ； 第二型最大概似估計 ； 均勻前驗分布 ； 單峰

並列摘要

For a Poisson process with a change-point, a uniform prior is commonly used for the change-point, but it is more realistic to put a unimodal prior on it, which outlines an important feature of prior beliefs. We consider a couple of unimodal priors on the change-point first and use ML-II approach to obtain the empirical Bayes estimators in this paper. The Bayes factor is used for the selection of a suitable prior. The procedure is applied to the British coal-mining disaster data. Finally, a comparison among these empirical Bayes estimators is made by Monte Carlo integration. It turns out that the ML-II Beta prior fit the data most, which corresponds to the prior belief of unimodality.

並列關鍵字

Bayes factor ； British coal-mining disaster data ； ML-II approach ； Uniform prior ； Unimodal

參考文獻

Bain, L. J.,Engelhardt, M.(1991).Statistical Analysis of Reliability and Lifetesting Models.New York:Marcel Dekker.

Good, I. J.(1983).Good Thinking: The Foundations of Probability and Its Applications.Minneapolis:University of Minnesota.

Jarrett, R. G.(1979).A note on the intervals between coal mining disasters.Biometrika.66,191-193.

Maguire, B. A.,Pearson, E. S.,Wynn, A. H. A.(1952).The time intervals between industrial accidents.Biometrika.39,168-180.

Rafery, A. E.,Akman, V. E.(1986).Bayesian analysis of a poisson process with a change-point.Biometrika.73,85-89.