- 學位論文
使用貝氏方法針對二項分配參數建立一些信賴區間之探討
Exploring Some of the Confidence Intervals for a Binomial Parameter Using Bayesian Approach
摘要
一直以來對於改善二項分配參數的信賴區間，就是學者欲求研究的課題，其中發展出了許多改善的方法，並加以互相討論比較，主要可分為古典與貝氏方法。而較合理的評判標準以包含機率與期望長度為主。 欲針對二項分配使用區間估計的方式估計參數「比例」，若使用一般傳統的標準信賴區間，在小樣本的條件下，往往所得的估計結果卻不如預期。本篇文章選取了標準、保守、威爾森和精確四種古典的區間估計方法和引用貝氏方法以無訊息先驗分配(non-informative prior)架構可靠區間，在小樣本的條件下與貝氏可靠區間作比較，並且探討各區間之特性，期望符合在真實包含機率(1- )以上的條件下，能達到改善，進而獲得一個適宜的信賴區間。
並列摘要
The simple problem of providing a confidence interval for the estimate of a binomial parameter can prove to be quite interesting. There are variety of competing intervals to choose from, using both frequentist and Bayes methods. A reasonable criterion for comparing these confidence intervals are coverage probability and expected length. For the estimate of a binomial parameter “Propotion”,the Standard approximate convidence interval has rather poor performance as we expected in small sample size condition. This article, we choose “Standard approximate” , ” Conservative”, ” Wilson”, ” Exact” and “Bayes credible with non-informative prior”. In this framework, we compare these confidence intervals performance with small sample size condition. In addition, we discusse each of these confidence intervals properties.we hope that we can fine a appropriate confidence interval to let the coverage probability reach confidence level (1- ) with sample size condition.
參考文獻
延伸閱讀
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