在指數分配中使用潛在貝氏因子與期望後驗貝氏因子做客觀的貝氏模型選擇

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簡文貴(Wen-kuei Jian) 查詢紙本館藏

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統計研究所

論文名稱

在指數分配中使用潛在貝氏因子與期望後驗貝氏因子做客觀的貝氏模型選擇
(Objective Bayesian Model Selection Using Intrinsic Bayes Factors and Expected Bayes Factors in Exponential Distributions)

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摘要(中)

使用貝氏方法做模型選擇或假設檢定時，經常無法使用一般的無資訊先驗分配。本篇論文將兩種客觀貝氏模型選擇法：潛在貝氏因子（Berger and Pericchi (1996c)）與期望後驗貝氏因子（Pérez and Berger (2002)）應用在指數分配模型選擇的問題上。這兩種方法都可以推導出客觀的先驗分配，分別稱為潛在先驗分配與期望後驗分配。利用這兩種方法所推導出來的先驗分配就可以當作“預設＂先驗分配直接用在相同領域所遭遇到的統計問題。
另外，本文也考慮在參數空間具有傘狀結構的條件下，利用期望後驗貝氏因子來決定傘頂位置。當資料來自K 個具有不同母體平均數的指數分配時，我們會使用期望後驗貝氏因子的方法找出傘頂位置。模擬的結果也證明我們所提出的方法可以提供準確的結果。

摘要(英)

In Bayesian approach to model selection or hypothesis, it is typically not possible to utilize standard noninformative distributions. In this thesis, we apply two objective Bayesian model selection methods, namely the intrinsic Bayes factor (Berger and Pericchi (1996c)) and the expected posterior Bayes factor (Péerez and Berger (2002)), to the problem of selecting models among exponential distributions. Both methods can deduce objective priors, called intrinsic prior and expected posterior prior, respectively, that can be used as a "default" prior directly to all the statistical problems encountered in the same scope.
We also consider that the parameter space has umbrella structure and utilize the expected posterior Bayes factors to decide the peak position. We will discuss the problem by using the expected posterior Bayes factor approach when the data are from k exponential distributions with different means. Simulation results show that the proposed algorithms provide accurate results.

關鍵字(中)

★ 期望後驗先驗分配
★ 潛在先驗分配
★ 客觀貝氏模型選擇
★ 期望壽命
★ 傘狀結構
★ 貝氏因子

關鍵字(英)

★ Bayes Factor
★ mean life time
★ objective Bayesian model selection
★ intrinsic prior
★ expected posterior prior
★ umbrella structure

論文目次

1 Introduction 1
1.1 Motivation and background . . . . . . . . . . . . . 1
1.2 Overview . . . . . . . . . . . . . . . . . . . . . 6
2 The Intrinsic Bayes Factors in Selecting the Largest Mean of the exponential Distributions 8
2.1 Review on intrinsic Bayes factors . . . . . . . . . 8
2.2 The intrinsic Bayes factors in selecting the largest mean of the exponential distributions . . . . . . . . . 11
2.3 Main results of intrinsic Bayes factors . . . . . . 14
2.3.1 Special case when k=3 . . . . . . . . . . . . . . 18
2.4 Simulation study on intrinsic Bayes factors . . . . 18
3 Expected posterior Bayes Factors in Selecting the Largest Mean of the Exponential Distributions 22
3.1 Review on expected posterior priors . . . . . . . . 22
3.2 The expected posterior Bayes factors in selecting the largest mean of the exponential distributions . . . . . 24
3.3 Main results of expected posterior priors . . . . . 27
3.3.1 Bayes factors . . . . . . . . . . . . . . . . . . 31
3.4 Simulation and example . . . . . . . . . . . . . . 33
4 The expected Posterior Bayes Factors in Selecting Exponential Distributions under Umbrella Structure 36
4.1 The expected posterior Bayes factors in selecting peak of means of the exponential distributions under umbrella structure . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Main results of expected posterior priors . . . . . 39
4.3 Simulation and example . . . . . . . . . . . . . . 44
5 Conclusion 48
Referneces 49

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指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2009-1-15

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