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研究生:林愉玶
研究生(外文):LIN,YU-PING
論文名稱:非誠實作答下兩階段隨機作答設計之貝氏推論
論文名稱(外文):Bayesian Estimation of Two-stage Randomized Reponses with Dishonesty Responses
指導教授:李燊銘李燊銘引用關係
指導教授(外文):LI,SHEN-MING
口試委員:呂恒輝謝淑惠
口試委員(外文):Lue,Heng-HuiHsieh,Shu-Hui
口試日期:2017-06-20
學位類別:碩士
校院名稱:逢甲大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:45
中文關鍵詞:隨機作答技巧敏感性問題貝氏估計馬可夫鏈蒙地卡羅吉氏抽樣性行為比例
外文關鍵詞:Randomized response techniqueSensitive questionBayesian estimationMarkov Chain Monte CarloGibbs samplingPropotion of sexual
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  在市場調查的過程中,經常會使用問卷調查方式蒐集數據,但若涉及到敏感性議題的調查時,若以直接問答方式,人們往往不願作答或為了保護自身隱私而不誠實作答,導致收集之數據偏誤,此時,問卷設計過程就顯得更為重要。
  Warner(1965)首先提出隨機作答設計(randomized response technique),以隨機作答模式保護受訪者隱私,增加誠實作答比例。Huang(2004)結合直接問答與Warner(1965)隨機作答方法,修正Warner(1965)之模型並增強敏感性特徵比例估計的有效性及提供具敏感性特徵的受訪者誠實回答的比例估計。在Huang(2004)中,使用最大概似估計法(MLE)估計誠實回答的比例或具敏感性特徵的比例時常會使估計落於(0,1)的區間外,而本文將沿用Huang(2004)之隨機作答設計模型,提出貝氏方法估計,並以馬可夫鏈蒙地卡羅法中(Markovn Chain Monte Carlo,MCMC)之吉氏抽樣(Gibbs sampling)程序此估計將會使估計值介於(0,1)之間。同時將使用統計模擬來比較Huang (2004)所使用的最大概似估計法與本文所提出的方法進行比較。
  最後,將使用在逢甲大學某系所收集之「性行為比例調查」數據實例,以貝氏估計法和最大概似估計法估計並比較,希望獲得更準確之估計。
 In the market survey, doing questionnaires is a general method to collect data.Nevertheless, the questions may involve sensitive issues, such as homosexual, sexual behavior, divorce and so forth.Furthermore, if doing directly response surveys, the results which are collected by questionnaires may lead to biased due to the respondents' self-privacy protection. Based on this reason,in order to protect the privacy of respondents and increase the proportion of honest replies,Warner (1965) proposed randomized response technique at first.After that, Huang (2004) combined directly response method and the randomized response technique, which effectively strengthens efficiency.Yet the use of maximum likelihood estimation may cause the estimation drops out of (0,1) interval.In this case, this paper proposes to use the model which is reported by Huang (2004) and estimates by Bayesian estimation.After that, this paper does Gibbs sampling in Markov Chain Monte Carlo (MCMC) process, thereby generating parameters and estimating it.
In addition, this paper compares the MLE of Huang(2004) with Bayesian estimating of this paper.Finally, this paper collects real data(The proportion of sexual behavior in a department of Feng Chia University) and compares the results estimating by MLE and Bayesian.
目錄
1 緒論
2 文獻探討
2.1 Warner(1965) 隨機作答設計
2.2 Chang and Huang(2001) 比例估計與敏感性的定性特徵
2.3 Huang(2004)
2.4 黃馨慧 , 鄭天澤 (2011) 貝氏方法應用於隨機作答模式之研究
2.5 劉怡均 , 李燊銘 , 彭德昭 , 高秀蘭 (2016) 貝氏分析應用在隨機作答技巧下
敏感性議題之比例估計
3 方法介紹
3.1 條件事後分配
3.2 貝氏推論程序
4 模擬估計
4.1 參數設定介紹
4.1.1 參數平均數
4.1.2 標準差估計
4.1.3 信賴區間與涵蓋率
4.2 貝氏事後樣本的相關性及收斂檢測
4.3 結果分析比較
5 實務應用
6 結論
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