Hidden Markov Processes : Theory and Applications to Biology
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 mostly from post-genomic biology, especially genomics and proteomics.
The topics discussed include standard material such as the Perron-Frobenius theorem, transient and recurrent states, stopping times, maximum likelihood estimation, and the Baum-Welch algorithm. The book contains extremely useful topics not usually seen at the basic level, such as mixing coefficients between random variables, ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC) methods, information theory, and introductory large-deviation theory. In the area of realization theory for hidden Markov models, the book presents contemporary research. Among biological applications, it presents an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory.