Hidden Markov Processes

丛 书 名：Princeton Series in Applied Mathematics

作     者：Vidyasagar M. 

I S B N：(纸本) 9780691133157 

出 版 社：Princeton University Press 

出 版 年：2014年

页      数：xiv, 287 pages :页

主 题 词：Markov processes. Computational biology. 

学科分类：0710[理学-生物学] 02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 09[农学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 070101[理学-基础数学] 

摘      要：This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are taken from post-genomic biology, especially genomics and *** topics examined include standard material such as the Perron-Frobenius theorem, transient and recurrent states, hitting probabilities and hitting times, maximum likelihood estimation, the Viterbi algorithm, and the Baum-Welch algorithm. The book contains discussions of extremely useful topics not usually seen at the basic level, such as ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC), information theory, and large deviation theory for both i.i.d and Markov processes. The book also presents state-of-the-art realization theory for hidden Markov models. Among biological applications, it offers an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory. Other applications such as profile hidden Markov models are also explored.