When sampling from multivariate distributions whose density contours are banana-shaped due to the non-linear correlation structure, traditional Markov chain Monte Carlo methods such as random walk Metropolis and independent Metropolis-Hastings suffer from severe low convergence. In this thesis, a model for bivariate banana-shaped distributions is constructed which is used to fit general banana-shaped distributions in terms of the probability density function. Transformations which are aimed at converting the variables to orthogonal variables by changing the coordinate system are designed for this distribution model. A new Markov chain Monte Carlo algorithm involving this set of transformations is proposed to sample these complex distributions. The key point of the new algorithm is to approximate the target density function using function using a parametric model which can facilitate the MCMC sampling after changing to another coordinate system. Detailed comparisons of convergence rate and estimation efficiency between the new method and existing methods are performed using both benchmark examples and practical examples, which showed the advantage of the new method. / 在多元概率分佈中，如果變量問存在非線性相關性使其等高線為香蕉形，傳統的馬爾科夫蒙特卡洛方法，如隨機漫步蒙特卡洛及獨立M-H方法都只有非常低的收斂速度和有效樣本數。本論文設計一種二元香蕉形分佈函數模型對一般香蕉形分佈進行擬合及一套能將其變量正交化的變換函數，並以此模型及變換函數為基礎建立一種新的馬爾科夫蒙特卡洛方法，實現對香蕉形分佈的高效率抽樣。該方法的關鍵在於對一般香蕉形分佈進行近似的參數模型能夠在進行坐標轉換後便於採樣。本論文將在不同例子中以收斂速度及估計效率為標準比較新方法與已有方法，模擬實驗和實例都顯示新方法較優。 / Chan, Kwun Cheung. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 50-52). / Abstracts also in Chinese. / Title from PDF title page (viewed on 05, October, 2016). / Detailed summary in vernacular field only.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_1291469 |
| Date | January 2014 |
| Contributors | Chan, Kwun Cheung (author.), Fan, Xiaodan (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Statistics. (degree granting institution.) |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography, text |
| Format | electronic resource, electronic resource, remote, 1 online resource (viii, 52 leaves) : illustrations (some color), computer, online resource |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons "Attribution-NonCommercial-NoDerivatives 4.0 International" License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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