Evaluation of Algorithms for Generating Dirichlet Random Vectors

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鄭經維(Ching-wei Cheng) 查詢紙本館藏

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統計研究所

論文名稱

Evaluation of Algorithms for Generating Dirichlet Random Vectors
(Evaluation of Algorithms for Generating Dirichlet Random Vectors)

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摘要(中)

在這篇文章中，我們提供一些用以生成 Dirichlet 隨機向量的演算法，並根據以下標準來評估這些演算法的表現：（一）電腦生成時間；（二）敏感度；以及（三）適合度。另外，我們特別檢驗一個基於 beta 變量轉換的演算法，並提供三個方針以減少此演算法的生成時間。模擬的結果顯示，除了所有（或大部分）的形狀變數都相當接近零的情況之外，基於我們所提出的方針整合而成的演算法顯著地在電腦生成時間上勝過其他的演算法。

摘要(英)

In this article, we describe various well-known Dirichlet generation algorithms and evaluate their performance in terms of the following criteria: (i) computer generation time, (ii) sensitivity, and (iii) goodness-of-fit. In addition, we examine in particular an algorithm based on transformation of beta variates and provide three useful guidelines so as to reduce its computer generation time. Simulation results show that the proposed algorithm outperforms significantly other approaches in terms of computer generation time, except in cases when all (or most) shape parameters are close to zero.

關鍵字(中)

★ 多維度適合度
★ 敏感度分析
★ 電腦生成時間
★ Dirichlet 隨機向量

關鍵字(英)

★ sensitivity analysis
★ multivariate goodness-of-fit
★ computer generation time
★ Dirichlet random vector

論文目次

1. Introduction ..................................... 1
2. Dirichlet Generation Algorithms .................. 3
2.1 Method Based on Order Statistics .............. 3
2.2 Multivariate Extension of J¨ohnk’s Method .... 4
2.3 Transformation Based on Gamma Variates ........ 4
2.4 Multivariate Acceptance-Rejection Methods ..... 5
2.4.1 The Uniform Proposal Density .............. 6
2.4.2 The Power Proposal Density ................ 7
2.5 Transformation Based on Beta Variates ......... 7
3. Performance Evaluation ........................... 13
3.1 Computer Generation Time ...................... 13
3.2 Sensitivity Analysis .......................... 17
3.3 Goodness-of-Fit ............................... 19
4. Concluding Remarks ............................... 22
Reference ........................................... 23
Appendix A. Calculations for rejection methods ...... 27
A.1 For algorithm Rejection-U ..................... 27
A.2 For algorithm Rejection-P ..................... 27

參考文獻

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指導教授

洪英超(Ying-Chao Hung)

審核日期

2009-6-18

推文