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針對p大n小時的貝氏變數選取 = Bayesian Variable S...

國立高雄大學統計學研究所

針對p大n小時的貝氏變數選取 = Bayesian Variable Selection for Large p Small n Problems

Record Type:	Language materials, printed : monographic
Paralel Title:	Bayesian Variable Selection for Large p Small n Problems
Author:	朱基祥,
Secondary Intellectual Responsibility:	國立高雄大學
Place of Publication:	[高雄市]
Published:	撰者;
Year of Publication:	2008[民97]
Description:	34面圖，表 : 30公分;
Subject:	Metropolis演算法
Subject:	Stochastic search variable selection
Online resource:	http://handle.ncl.edu.tw/11296/ndltd/86138862850223905439
Notes:	指導教授：陳瑞彬
Notes:	參考書目：面27-28
Summary:	在貝氏變數選取的方法中，馬可夫鏈的蒙地卡羅演算法是常被用來得到事後樣本。通常馬可夫鏈的蒙地卡羅演算法在每一個反覆的步驟中均需要計算一個p×p的事後相關矩陣，其中p為候選的迴歸因子個數。然而，計算一個反矩陣是成本相當昂貴的，特別是當候選的迴歸因子個數很多的時候。為了降低計算上的花費，陳和賴(2007)提出兩個有效率的隨機選取方法。他們成功的將這兩個方法應用在n大p小的情況。基於這兩個變數選取方法，我們做了一些修改而提出兩個貝氏選取的方法。除了應用在n大p小的情況，我們將焦點放在p大n小的問題上。這裡我們會舉出一些模擬和實際的例子來驗證我們所提出新的貝氏選取方法的效能。從我們的模擬結果可以看出我們的方法有很好的效能。 In Bayesian variable selection methods, MCMC algorithms are used toobtained the posterior samples. Usually at each iteration these MCMCalgorithms require computing a p×p posterior covariancematrix, where p is the number of the potential regressors.However, the computational cost of computing inverse matrices isvery expensive, especially when p is large. In order to avoidcomputing inverse matrices, Chen and Lai (2007) have proposed twoefficient stochastic variable selection procedures. Theysuccessfully applied these two stochastic methods in to the cases oflarge n and small p. Based on these two procedures, some minormodifications are made, and then we propose two new Bayesianalgorithms. Besides the case of large n and small p, we are alsointerested in the problems of large p and small n. Severalsimulations and real examples are used to show the performances ofour new Bayesian algorithms. From our simulation results, these twoalgorithms work well.

針對p大n小時的貝氏變數選取 = Bayesian Variable Selection for Large p Small n Problems
朱, 基祥

針對p大n小時的貝氏變數選取 = Bayesian Variable Selection for Large p Small n Problems / 朱基祥撰 - [高雄市] : 撰者, 2008[民97]. - 34面 ; 圖，表 ; 30公分.
指導教授：陳瑞彬參考書目：面27-28.
Metropolis演算法Stochastic search variable selection

針對p大n小時的貝氏變數選取 = Bayesian Variable Selection for Large p Small n Problems
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330 $a 在貝氏變數選取的方法中，馬可夫鏈的蒙地卡羅演算法是常被用來得到事後樣本。通常馬可夫鏈的蒙地卡羅演算法在每一個反覆的步驟中均需要計算一個p×p的事後相關矩陣，其中p為候選的迴歸因子個數。然而，計算一個反矩陣是成本相當昂貴的，特別是當候選的迴歸因子個數很多的時候。為了降低計算上的花費，陳和賴(2007)提出兩個有效率的隨機選取方法。他們成功的將這兩個方法應用在n大p小的情況。基於這兩個變數選取方法，我們做了一些修改而提出兩個貝氏選取的方法。除了應用在n大p小的情況，我們將焦點放在p大n小的問題上。這裡我們會舉出一些模擬和實際的例子來驗證我們所提出新的貝氏選取方法的效能。從我們的模擬結果可以看出我們的方法有很好的效能。 In Bayesian variable selection methods, MCMC algorithms are used toobtained the posterior samples. Usually at each iteration these MCMCalgorithms require computing a p×p posterior covariancematrix, where p is the number of the potential regressors.However, the computational cost of computing inverse matrices isvery expensive, especially when p is large. In order to avoidcomputing inverse matrices, Chen and Lai (2007) have proposed twoefficient stochastic variable selection procedures. Theysuccessfully applied these two stochastic methods in to the cases oflarge n and small p. Based on these two procedures, some minormodifications are made, and then we propose two new Bayesianalgorithms. Besides the case of large n and small p, we are alsointerested in the problems of large p and small n. Severalsimulations and real examples are used to show the performances ofour new Bayesian algorithms. From our simulation results, these twoalgorithms work well.
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