貝氏模型平均演算法及其在長時期追蹤資料之應用

王國肇(Guo-Tzau Wang)

指導教授 ： 樊采虹

國立中央大學/理學院/統計研究所/碩士(2007年)

摘要

本文將貝氏模型平均法做一改良，提出模型漫步演算法以遞迴搜尋的方式選取模型，模擬結果顯示，在一般線性迴歸模型下，其平均被遺漏模型的後驗機率總和比傳統奧坎氏視窗法中所有遺漏的模型之後驗機率總和低；另外在選用不當的初始模型時，與使用較佳初始模型相較，模型漫步演算法所多耗費的計算量遠比奧坎氏視窗法少，且遺漏的模型也較少，亦即我們提出的演算法較不受限於初始模型的選擇。另外，配合吉比氏抽樣法將模型漫步演算法應用在具 AR(1) 誤差模型之長時期追蹤資料迴歸模型中，並將其應用在颱風降雨量之預測上。

關鍵字

奧坎氏視窗法 ； AR(1)模型 ； 吉比氏抽樣法 ； 長時期追蹤資料 ； 貝氏模型平均

並列摘要

In this thesis, we propose a new recursive algorithm, namely the model walking algorithm, to modify the widely used Occam''s window method in Bayesian model averaging procedure. It is verified, by simulation, that in the regression models, the proposed method is much more efficient in terms of computing time and the selected candidate models. Moreover, it is not sensitive to the initial models. We then apply Bayesian model averaging to the multiple longitudinal regression models with AR(1) random errors within subjects. Gibbs sampling method together with the model walking algorithm are employed. The proposed method is also successfully used to make rainfall prediction based on typhoon data in Taipei, Taiwan.

並列關鍵字

AR(1) ； Occam''s window ； Gibbs sampling ； longitudinal data ； Bayesian model averaging

參考文獻

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