在幾何學上的污染下使用發散性測量局部敏感性

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Title:	在幾何學上的污染下使用發散性測量局部敏感性
Authors:	婁國仁;Lou, Kuo-ren
Contributors:	淡江大學經營決策學系
Keywords:	貝氏因子;貝氏穩健性;敏感度量測;微敏感性;干擾;總變異量;發散性;加權分配;Bayes Factor;Bayes Robustness;Sensitivity Measurement;Infintiesimal Sensitivity;Perturbation;Total Variation;Divergence;Weighted Distribution
Date:	2002-04
Issue Date:	2009-11-30 13:37:44 (UTC+8)
Abstract:	對事前分配(Prior)的選擇，貝式程序的敏感性是很多貝式研究者關心的主題。傳統上，在貝式推論裡的敏感度分析或穩健議題上被分成兩大類－整體的與局部的敏感性。在整體性的分析裡，考慮在一組合理的事先分配中研究事後(Posterior)特徵的變化，然而在局部性分析裡是探討以某一被引出的(相信的)事前分配，在其附近做小干擾，觀察其影響性。不管怎樣，貝式分析強烈地依賴模型的假設，利用事前與概似 (Likelihood)的運用。本論文中、我們探討雙重干擾(事前且/或概似)的作用影響在事後推論上。尤其，我們開發局部敏感性測度，為了同時對兩者作干擾，觀察事後敏感性如何。然後，將其作幾何學上的型態干擾，使用發散性測度，應用在加權分配問題上，取得局部敏感性的結果。 The sensitivity of Bayes procedures to the choice of a priordistribution is a major concern for many Bayesians. Traditionally, thesensitivity analysis or the robustness issues in Bayesian inferencecan be classified into two broad categories, global and localsensitivity. In global analysis, one considers a class of reasonablepriors and studies the variations of posterior features, whereas inlocal analysis, the effects of minor perturbations around someelicited priors are studied. However, a Bayesian analysis stronglydepends on modeling assumptions which make use of both prior andlikelihood. In this paper we investigate the effects of dualperturbations (prior and/or likelihood) on the posterior inference. Inparticular, we develop local sensitivity measures to detect howsensitive the posterior is with respect to simultaneous perturbationsin both prior and likelihood. Local sensitivity measures are obtainedusing the notion of divergence measures for geometric type ofperturbations with weighted distribution problems.
Relation:	2002年兩岸管理科學暨經營決策學術研討會論文集，頁271-280
Appears in Collections:	[Department of Management Sciences] Proceeding

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