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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/3853


    Title: 非均質波松過程的後驗常態性(2/2)
    Other Titles: Posterior Normality for Nonhomogeneous Poisson Processes (II)
    Authors: 翁久幸
    Keywords: 非均質波松過程;隨機過程;後驗分配
    Stochastic processes;Posterior distribution;Posterior normality;Stein`s identity
    Date: 2001
    Issue Date: 2007-04-18 16:36:49 (UTC+8)
    Publisher: 臺北市：國立政治大學統計學系
    Abstract: 過去許多研究指出,某些隨機過程的未知參數之後驗分配近似於常態.相關之研究如 Heyde and Johnstone (1979,以下簡 稱 H-J), Basawa and Rao (1980). 其中, H-J 提出一組條件,並證明對於一般隨機過 程,只要滿足這些條件,則其參數之後驗分 配近似於常態. 不幸的, 某些reliability 上常見的非均質波松過程 (nonhomogeneous Poisson processes,以下簡稱 NHPPs)並不符合這組條件.有鑑於此, Sweeting and Adekola (1987)把 H-J 的條件加以放寬與修改, 並證明這組新的 條件涵蓋更多的模型,包括若干出生過程 (birth processes)及上述之 NHPPs 模型. 以上的研究多半以機率密度函數的展開 來看後驗分配的問題.在這個計畫中,我修 改 Stein ’s Identity 來討論未知參數之後驗分配的問題.這裡提到 的 Stein`s Identity 乃由 Woodroofe (1989)所提出. 這個 Identity 可以把後驗期望值作展開. 此展開式的首項與標準常態的結果相同,而餘項在樣本愈大時愈近似零. 之前的結果只局限於均 質的過程.我把這個Identity 修改後,就可以用於非均質過程.我們給予一般性證明之後,也分別討論其應用於上述之NHPPs模型以及 conditional exponential family 之情形. 我們的證明尚稱簡潔, 所要求的條件也適中.
    We propose a new method to derive the posterior normality of stochastic processes. For a suitable parameter transformation Zt, the likelihood function is converted into a form close to a standard normal density. Then we propose a modified version of Stein`s Identity and apply it to obtain an expression for the posterior expectation of h(Zt). From this, posterior normality of Zt can be established. Applications of this method are illustrated by the conditional exponential family and a nonhomogeneous Poisson process.
    Description: 核定金額：203000元
    Data Type: report
    Appears in Collections:[統計學系] 國科會研究計畫

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