混合的偏斜常態分布其及應用

Abstract

混合的常態分佈對於來自不同來自母體的異質性資料提供了一種的自然模型架構。近二十年來， 偏斜的常態分佈對於處理非對稱的資料問題已被驗證是一種很有用的工具。 本文我們提出了以概似函數與貝氏抽樣為基礎之方法去處理混合偏斜常態分佈的問題。 我們將利用＂期望最大值型式＂(EM-type)演算法求最大概似估計值。

對於所提出的先驗分佈及所推導之後驗分佈的結果, 我們也運用馬可夫鏈蒙地卡羅發展出貝氏的計算方法。 最後我們透過兩個實例來闡述所提出模型之應用。

The normal mixture model provides a natural framework for modelling the heterogeneity of a population arising from several groups. In the last two decades, the skew normal distribution has been shown to be useful for modelling asymmetric data in many applied problems. In this thesis, we propose likelihood-based and Bayesian sampling-based approaches to address the problem of modelling data by a mixture of skew normal distributions.EM-type algorithms are implemented for computing the maximum likelihood estimates. The prior as well as the resulting posterior distributions are developed for Bayesian computation via Markov chain Monte Carlo methods.Applications are illustrated through two real examples.