Bayesian Analysis of a change-point Poisson Process

布瓦松過程具轉折點之貝氏分析

10.6595/BDCM.2007.2(2).1

林億雄(Yi-Hsiung Lin)；任眉眉(Mei-Mei Zen)

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

致遠管理學院學報

2_2期（2007 / 09 / 01）

1 - 15

英文

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。

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.

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