逐步型I區間設限資料的貝氏分析

The MCMC Approach to Progressive Type-I Interval Censoring Data

許文志(Wen-Chih Hsu)

指導教授 ： 林余昭

中原大學/理學院/應用數學研究所/碩士(2010年)

https://doi.org/10.6840/cycu201000543

摘要

首先我們假設逐步型I 區間設限資料來自於兩參數的廣義指數(Generalized Exponential, GE) 分配。接著介紹一些現有的方法, 例如最大概似估計法(MLE) 及期望最大化(EM) 演算法等, 並對資料進行統計推估。之後, 我們試著在逐步型I 區間設限資料下,運用馬可夫鏈蒙地卡羅(MCMC) 法。
我們模擬資料來研究各種不同估計法之統計分析, 顯示結果在不含任何參數訊息的先驗分配下, 用MCMC 法所獲得的估計結果, 與使用MLE 法下的估計結果相當接近。但是, 其缺點是它必須花費較長時間去跑MCMC 抽樣模擬。然而, 如果能夠提供關於參數的訊息, 對於貝氏分析將會更好的效果。
最後, 我們使用實際資料Carbone et al. (1967), 來對模型參數做評估。

關鍵字

廣義指數分配 ； 馬可夫鏈蒙地卡羅法 ； 逐步型I 區間設限 ； 期望最大化演算法 ； 最大概似估計法

並列摘要

Assume the progressive type-I interval censoring data come from two parameter generalized
exponential distribution. We first introduce some existing methods, such as the
Maximum likelihood estimate (MLE) and the Expectation-Maximization (EM) algorithm,
to do statistical estimation. Then, we study progressively type-I interval censoring data
by the Markov chain Monte Carlo (MCMC) method.
Simulated data are generated to investigate the performances of all estimation methods.
It shows that the estimation obtained by our MCMC method with non-informative
priors is about as good as that by the MLE, but its disadvantage is that it takes longer time
to run the MCMC samplers. However, if some prior information about the parameters is
given, the Bayesian approach is better.
Finally, a real data set, Carbone et al. (1967), is applied by our developed MCMC
approach.

並列關鍵字

Maximum likelihood estimate ； Expectation-Maximization algorithm ； Markov Chain Monte Carlo ； Progressive type-I interval censoring ； Generalized exponential distribution

參考文獻

[1] Aggarwala, R. (2001) , “Progressively interval censoring: some mathematical results

[2] Balakrishnan, N. and Aggarwala, Rita (2000) , “Progressive Censoring: Theory,

Wiley Series in Probability and Statistics.

[5] Gupta, R. D. and Kundu, D. (2001a) , “Exponentiated exponential distribution: An

alternative to gamma and Weibull distributions”, Biometrical Journal, 43:117-130.