重複捕取資料在族群數估計時不同的先驗分布對後驗分布推論的敏感度之研究

On sensitivity of posterior inference to various priors in population size estimation through capture-recapture method - a simulation study

張佳惠(Chia-Hui Chang)

指導教授 ： 彭雲明

國立臺灣大學/生物資源暨農學院/農藝學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.03039

摘要

生態學家研究族群有許多不同的動機。其中包含族群的研究能有效監測瀕危物種、控制有害物種族群,和管理獵物族群。另外也能提供線索以了解、控制疾病的流行。

本研究是對於一封閉族群重複捕取資料估算族群數,分別以不同的先驗分布進行貝氏估計。自1990年代中期,生態統計學家傾向接受貝氏理論,因為貝氏統計將未知參數看做一隨機變數,此觀點較符合生態現象。而動物被捕捉的機率會隨著時間變化、隨個體行為反應而改變以及隨個體間變異而改變;本研究討論捕捉機率隨時間而改變之重複捕取模式(Mt 模式);在重複捕取模式下,分別考慮reference prior為(0,0),(0.5,0.5),(1,1)的貝它分布及Empirical Bayes作為捕取機率 π(pi) 之先驗分布的參數,
將後驗平均值(posterior mean)當作貝氏估計式。

模擬實驗模仿sunfish和cottontail rabbit重複捕取資料執行族群數的估算,發現改變先驗分布的參數,明顯的影響後驗分布,從估計的族群數均方差(MSE)和最大後驗密度(HPD)可信區間觀察到先驗分布對後驗分布的影響,此變化稱為敏感度;欲研究重複捕取次數改變,不同的先驗分布是否對後驗分布造成不同的敏感度。我們以變異係數(C.V.)加以討論。
最後,我們將sunfish和cottontail rabbit在重複捕取實驗下所得數據執行資料分析。

關鍵字

貝氏推論 ； 重複捕取模式 ； 無訊息先驗分布 ； 共軛先驗分布 ； 最大後驗密度可信區間

並列摘要

Ecologists study populations for many reasons. Population studies hold the key to saving endangered species, controlling pest populations, and managing game populations. They also offer clues to understanding and controlling disease epidemics.
Finally, the greatest environmental challenge to biological diversity and the integrity of the entire biosphere is at its heart a population problem.

Bayesian inference was introduced to the wild life population size estimation in the early 1980. Through the years statisticians keep putting efforts on incorporating the Bayesian way of estimation into the well-known capture-mark-recapture method.
Though the progress in this area of research is achieved, there are still some questions unanswered. One of them is the magnitude of impact caused by various priors on the sensitivity of posterior inference. The author tries to approach this question by simulation study. Two different scenarioes are set for the simulation study; one is for large number of recaptures; the other less number of recaptures. The results show that number of recaptures are critical to the sensitivity of posterior inference. Large variation of posterior mean is associated with large number of recaptures while the number of recaptures is small the corresponding variation is also reduced.

並列關鍵字

Bayesian inference ； capture-recapture model ； noninformative prior distribution ； conjugate prior distribution ； HPD

參考文獻

Castledine, B.J. (1981). A Bayesian analysis of multiple-recapture sampling for a closed population. Biometrika 67, 197-210.

Darroch, J.N.(1958). The multiple-recapture census, I: Estimation of a closed population. Biometrika 63, 343-359.

Edward, I.G., and Christian, P.R. (1992). Capture-recapture estimation via Gibbs sampling. Biometrika 79, 677-683.

Lee, P.M. (1997). Bayesian Statistics: An Introduction . Second edition.

New York: Oxford University Press.