Hidden Markov processes : theory and applications to biology / M. Vidyasagar.

Format:

Book

Author/Creator:

Vidyasagar, M. (Mathukumalli), 1947- author.

Series:

Princeton series in applied mathematics.

Princeton Series in Applied Mathematics

Language:

English

Subjects (All):

Computational biology.

Markov processes.

Physical Description:

1 online resource (303 p.)

Edition:

Course Book

Place of Publication:

Princeton, New Jersey ; Oxford, England : Princeton University Press, 2014.

Language Note:

English

Summary:

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 proteomics. The 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.

Contents:

Front matter

Contents

Preface

PART 1. Preliminaries

Chapter One. Introduction to Probability and Random Variables

Chapter Two. Introduction to Information Theory

Chapter Three. Nonnegative Matrices

PART 2. Hidden Markov Processes

Chapter Four. Markov Processes

Chapter Five. Introduction to Large Deviation Theory

Chapter Six. Hidden Markov Processes: Basic Properties

Chapter Seven. Hidden Markov Processes: The Complete Realization Problem

PART 3. Applications to Biology

Chapter Eight. Some Applications to Computational Biology

Chapter Nine. BLAST Theory

Bibliography

Index

Back matter

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781400850518

1400850517

OCLC:

885122066