右設限資料下貝氏對勝算比之研究

此篇論文是利用伯氏多項式來描述勝算比，使用貝氏方法對右設限資料之分析，並以馬可夫鏈蒙地卡羅法去估計勝算比。本篇論文架構如下。第一節，緒論。第二節，因勝算比函數是一個遞增函數，所以我們用伯氏多項式來描述它。第三節，資料介紹，並從其資料可推導概似函數，進而得到貝氏推論。第四節，我們論文提供了兩個演算法：遞增之演算法及凹口向下且遞增之演算法。第五節，我們用這兩種演算法來比較，所得的模擬結果顯示資料越大、估計會越準確，也符合我們的大樣本性質，當知道真正的勝算比函數的圖形為凹口向下，我們用凹口向下遞增演算法會比遞增演算法估得較準確。

關鍵字

右設限；勝算比；貝氏方法；伯氏多項式

並列摘要

The essay makes use of Bernstein polynomials to discribe the odds rate. It analysises the right-censored data with Bayesian estimation to estimate odds rate with Markov chain Monte Carlo. Here is the frame structure. The first chapter is the introduction. Because the odds rate is a increasing function,we try to describe it with Bernstein polynomials in Chapter Two. It’s going to introduce the data to get the likelihood function,and to get Bayesian approach in Chaper Three. We can get two algorithms from the essay,increasing algorithm and,concave down and increasing algorithm,in Chapter Four. In Chapter five,we use these two algorithms to compare simulation results show that data obtained from larger,estimates will be more accurate,is also in line with our properties of large sample. When we realize that the shape of true odds rate function is concave down,we use concave down and increasing algorithm,estimate more accurate than the increasing algorithm.

並列關鍵字

right-censored ； odds ratio ； bayesian estimation ； bernstein polynomials

參考文獻

[5 ] 王聖文 (2007) 貝氏存活分析之右設限資料之研究，中原大學碩士

[6 ] 黃志誠 (2011) 貝氏存活右設限資料風險函數之研究，中原大學碩

[2 ]G. Casella , R.L. Berger ” Statistical inference ” , Duxbury Press 1990.

[3 ]Christian P. Robert, George Casella ” Monte Carlo Statistical Methods

[4 ]P. Green ” Reversible jump Markov chain Monte Carlo computation and

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右設限資料下貝氏對勝算比之研究

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