关于隐马尔科夫模型的探讨.pdfVIP

摘 要 隐马尔科夫模型的相关理论早在19世纪就已经由俄国有机化学家Vladimir V.  Markovnikov 提出，但是模型的应用在最近的十几年才随计算机的发展而得到关 注和研究。隐马尔科夫模型在很多重要的领域中得以应用和发展，包括信息工 程，生物和医学等等科学领域。  大部分关于隐马尔科夫模型的应用都是基于离散时间马尔科夫理论。本文将 主要探讨连续时间隐马尔科夫模型的理论及应用。首先文章给出了连续时间隐 马尔科夫模型的理论，并将协变量引入模型，作为影响误判概率模型的因素。 接着本文通过不同角度的模拟实验，对隐马尔科夫模型的拟合优度进行了探讨， 并对隐马尔科夫模型的适用条件提出了建议。  最后本文还通过隐马尔科夫模型，在存在筛选误判情况下为心脏移植病变进 展建立模型，深入分析了该病的进展规律，各个阶段逗留时间等方面的问题。      关键字：转移强度矩阵，误判概率矩阵，隐马尔科夫模型    Abstract Though the relevant theory of Hidden Markov Model has been introduced early in the 19’s Century by Russian organic chemist, its population has just begin as the development of computer. There are applications of Hidden Markov Model in variety of research field, including Signial processing, Biological sequencing as well as Medical application. In most of the application of Hidden Markov Model, the time scale was discrete, this thesis will focus on the continuous-time Markov Models. Firstly, the theory of Hidden Markov Model in continuous-time scales will be presented and covariates will be introduced into the model as the factor of influencing the misclassification probability. Secondly, a series simulation will be performed from different aspects to study the goodness of fit of Hidden Markov Model, and some advise of applying the model will be proposed as the conclusion of the simulation. Finally, application of Hidden Markov Model to screening coronary allograft vasculopathy will be present, modeling and analysis based on the model of the progression of the disease also will be discussed. Keywords: Transition Intensity Matrix, Misclassification Probability Matrix, Hidden Markov Model   目 录 第1 章 引言 1