常態母體間平均數具傘形限制之貝氏選模

A Bayesian Model Selection for Umbrella Restriction among Normal Means

樊采虹(Tsai-Hung Fan) ； 鄭庭芳(Ting-Fang Cheng)

《中國統計學報》 42卷1期 (2004/03) Pp. 63-80

https://doi.org/10.29973/JCSA.200403.0004

摘要

設限參的問題近來被各方廣泛的應用，包括類別資料 ( ordinal categorical data )，精算分級 ( actuarial graduation ) ，生物鑑定 ( bioassay ) 等，本文考慮在常態母體間平均數具傘形限制時，根據資料欲找出傘頂的位置，以決定資料最支持的模型；在參數具傘形限制的條件下，隨著傘頂位置的不同，可將其視為不同的模型，我們以貝氏因子法則 ( Bayes factor criterion ) 來決定最適模型，並以蒙地卡羅積分法 ( Monte Carlo integration ) 計算各模型之後驗機率，進而對各參數進行貝氏估計。

關鍵字

傘型限制 ； 貝氏因子 ； 蒙地卡羅積分

並列摘要

Restriceted parameter space problems have been considered widely in various statistical applications such as ordinal catergorical data, actuarial graduation and bioassay. In this paper, we consider several normal populatons with umbrella-type restrion among their means and we want to determine which population has the largest mean. A Bayesian model selection method is used to locate the largest population. Simple Monte-Corlo integration is used calculate the posterior probability of each possible model as well as the Bayesian point estimation of each parameter.

並列關鍵字

Bayes factor ； Monte-Chrlo integration ； umbrella restriction

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