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研究生:賴駿騰
研究生(外文):Jun-Teng Lai
論文名稱:二維指數分配之貝氏分析
論文名稱(外文):Bayesian Analysis of Moran–Downton Bivariate Exponential Distribution
指導教授:林余昭
指導教授(外文):Yu-Jau Lin
學位類別:碩士
校院名稱:中原大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:中文
論文頁數:43
中文關鍵詞:貝氏統計馬可夫鏈蒙地卡羅法R2OpenBUGS 套件
外文關鍵詞:Bayesian statisticsMarkov chain Monte Carlo methodR2OpenBUGS package
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貝氏統計分析已廣泛應用在醫學、教育、工業等領域,雖然以往受限於計算較為複雜,但隨著科技的進步,許多相關統計軟體的出現,統計學者可以利用過去的經驗,再結合蒐集的資訊進行分析與模擬,然而這些問題得到了解答,使得貝氏統計越來越受到重視。利用 OpenBUGS 軟體可以有效的執行馬可夫鏈蒙地卡羅法來估計模型的參數。本文要討論 Moran-Downton 二維指數分配參數的貝氏估計過程,當正確的使用已知的訊息,再對參數進行迭代後,再觀察參數的估計值是否逼近參數的真實值。所以本文以 R 軟體的 R2OpenBUGS 套件來對 Moran-Downton 二維指數分配的模型進行參數的貝氏統計分析。在 R 的環境下處理資料較為方便,再利用 R2OpenBUGS 套件執行貝氏統計的參數估計。
The Bayesian analysis has many applications in almost all fields, such as education, medical treatments, quality control, and so on. But the computation of Bayesian statistics is more complicated compared to the
frequentists statistics since the statisticians usually need to write the programs codes to apply MCMC method.
In this thesis, we consider the Bayesian approach of Moran-Downtown bivariate Exponential (DBE) model and analyze the data using OpenBUGS. The freeware OpenBUGS is a popular Bayesian software with a simple language
syntax, but its interface is tedious in data analysis and simulation study.
We first simulate the bivariate data from the model and use the R package,R2OpenBUGS, to call OpenBUGS from R console to analyze both the simulated data and real data. The difficulty of this research is that the probability density of DBE model consisting of modified Bessel function is not standard in the BUGS language. We successfully use the Zero trick to describe the DBE alternative likelihood in terms of a sum of geometric and gamma functions.
論文目錄
摘要...i
Abstract...ii
謝誌...iii
論文目錄...iv
表目錄...vi
圖目錄...vii
第一章 緒論
1.1 研究背景...1
1.2 論文架構...2
第二章 模型
2.1 Moran-Downton 二維指數分配...3
第三章 研究方法
3.1 貝氏統計...9
3.2 MCMC...10
3.3 馬可夫鏈...10
3.4 蒙地卡羅積分...11
3.5 M-H 演算法...12
3.6 Gibbs 抽樣法...12
第四章 軟體介紹與應用
4.1 BUGS...14
4.2 R 語言...15
4.3 R2OpenBUGS 套件...15
第五章 範例與實作模擬
5.1 貝氏分析範例...18
5.2 模型模擬與分析...20
5.3 實例分析...32
第六章 結論...34
參考文獻...35

表目錄
表 4.1 常用的 BUGS 函數...16
表 4.2 常用的 BUGS 機率分配...17
表 5.1 模擬 λ1 估計值...30
表 5.2 模擬 λ2 估計值...30
表 5.3 模擬 ρ 估計值...31

圖目錄
圖 5.1 λ1(樣本數 N = 20)...24
圖 5.2 λ2(樣本數 N = 20)...24
圖 5.3 ρ(樣本數 N = 20)...25
圖 5.4 λ1(樣本數 N = 50)...25
圖 5.5 λ2(樣本數 N = 50)...26
圖 5.6 ρ(樣本數 N = 50)...26
圖 5.7 λ1(樣本數 N = 100)...27
圖 5.8 λ2(樣本數 N = 100)...27
圖 5.9 ρ(樣本數 N = 100)...28
圖 5.10 λ1(樣本數 N = 200)...28
圖 5.11 λ2(樣本數 N = 200)...29
圖 5.12 ρ(樣本數 N = 200)...29
Hastings, W. K. 1970. Monte Carlo Sampling Methods Using Markov Chains andTheir Applications, Biometrika, 57, 97-109.

Metropolis, N., Rosenbluth, A. W., Rosenbluth,M. N. , Teller,A. H., and Teller, E.1953. Equations of State Calculations by Fast Compution Machines, Journal of
chemical Physics, 21, 1087-1091.

Geman, S. and Geman, D. (1984). Stochastic Relaxation, Gibbs Distribution and the Bayesian Restoration of Images. IEEE Trans. Patten Ann., Machine Intell.,6,721-741

Gelfand,A. E. and Smith, A. F. M. (1990).Sampling-Based Approaches to Calculating Marginal Densities. J. Am. Statist. Assoc., 85,398-409.

F. Downton, Bivariate exponential distributions in reliability theory, J. R. Stat. Soc. Ser. B 32 (1970), pp. 408-417.

W.F. Kibble, A two-variate gamma type distribution, Sankhy`a 5 (1941), pp. 137-150.

Kibble, W. F. (1941). A two-variate gamma type distribution. Sankhy˜a, 5, 137–150.

Kotz, S., Balakrishnan, N. and Johnson, N. L. (2000). Continuous Multivariate Distributions,
1, Second edition. New York, Wiley.

Iliopoulos, G. and Karlis, D. (2003). Simulation from the Bessel distribution with applications. Journal of
Statistical Computation and Simulation, 73, 491–506.
54, 385–394.

Al-Saadi, S. D. and Young, D. H. (1980). Estimators for the correlation coefficient in a
bivariate exponential distribution. J. Statist. Comput. Simul., 11, 13–20.

Al-Saadi, S. D. and Young, D. H. (1982). A test for independence in a multivariate exponential distribution with equal correlation coefficient. J. Statist. Comput. Simul.,14, 219–227.

Balakrishnan, N. and Ng, H. K. T. (2001). Improved estimation of the correlation coefficient
in a bivariate exponential distribution. J. Statist. Comput. Simul., 68, 173–184.

Tierney, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22, 1701-
1762.

Nagao, M. and Kadoya, M. (1971). Two-variate exponential distribution and its numerical table for engineering application,Bulletin of the Disaster Prevention Research Institute,20, No. 3, 183–215.

Kundu, D. and Gupta, R (2009). Jounral of Multivariate Analysis, Vol 100, Issue 4, p 581-593.
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