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| Title: | 以高效率狄氏演算法產生其他機率分配
Generation of Distributions Based on an Efficient Dirichlet Algorithm |
| Authors: | 陳韋成
Chen, Wei Cheng |
| Contributors: | 洪英超
Hung, Ying Chao
陳韋成
Chen, Wei Cheng |
| Keywords: | 狄氏分配
多面體均勻分配
反狄氏分配
Liouville分配
蒙地卡羅模擬
方區抽樣
Dirichlet distributions
uniform distributions over polyhedrons
Inverted Dirichlet distributions
Liouville distributions
Monte Carlo simulation
quadrats sampling |
| Date: | 2012 |
| Issue Date: | 2013-07-11 16:37:08 (UTC+8) |
| Abstract: | 狄氏分配(Dirichlet distribution)可視為高維度的貝他分配，其應用範圍包括貝氏分析的共軛先驗分配，多變量資料建模。當狄氏分配參數α_1=⋯=α_(n+1)=1時，可視為在n維空間的單體(simplex)均勻分配。高維度空間的不規則區域均勻分配有很多的應用，例如：在不規則區域中物種調查的方區抽樣和蒙地卡羅模擬(Monte Carlo Simulation)常需要多面體的均勻亂數，利用狄氏分配可更迅速的生成不規則區域的均勻亂數。本論文主要是評估由Cheng et al. (2012) 設計的R統計軟體套件“rBeta2009” [8]，並探討如何利用此套件中的狄氏分配演算法來生成其他多變量分配，如：(i)反狄氏分配(Inverted Dirichlet distribution) (ii) Liouville分配，以及(iii)由線性限制式所圍成的多面體空間之均勻分配。本文也利用電腦模擬的方式驗證本文介紹之方法比現有的電腦軟體中的演算法有效率(以電腦執行時間來看)。
Dirichlet distributions can be taken as a high-dimensioned version of beta distributions, and it has many applications, such as conjugate prior distribution in bayesian Inference and construction of the model of multivariate data. When the parameters of Dirichlet distributions are α_1=⋯=α_(n+1)=1, it can be regarded as uniform distribution within a n-dimensioned simplex. High-dimensioned uniform distribution in irregular domains has various applications, such as species surveys in quadrats sampling and Monte Carlo simulation, which often need to generate uniform random vectors over polyhedrons. With Dirichlet distributions, it is more efficient to generate uniform random vectors in irregular domain. This article evaluated the module in R, “rBeta2009” [8], originally designed by Cheng et al. (2012), and discusses how to generate other multivariate distributions by using the Dirichlet algorithm in the package, including generation of (i) Inverted Dirichlet random vectors (ii) Liouville random vectors, and (iii) uniform random vectors over polyhedrons with linear constraints. The article also verified that the method is more efficient than the older package in R. (by comparing the CPU time.) |
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| Description: | 碩士
國立政治大學
統計研究所
100354025
101 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0100354025 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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