Hidden Markov processes : (Record no. 43856)

MARC details
000 -LEADER
fixed length control field 06527cam a2200301 i 4500
003 - CONTROL NUMBER IDENTIFIER
control field CUTN
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20241122112220.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 140325t20142014njua b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780691133157 (hardcover : acidfree paper)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0691133158 (hardcover : acidfree paper)
041 ## - LANGUAGE CODE
Language English
042 ## - AUTHENTICATION CODE
Authentication code pcc
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 570.285
Edition number 23
Item number VID
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Vidyasagar, M.
245 10 - TITLE STATEMENT
Title Hidden Markov processes :
Remainder of title theory and applications to biology /
Statement of responsibility, etc M. Vidyasagar.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Princeton,
Name of publisher, distributor, etc Princeton University Press,
Date of publication, distribution, etc 2014.
300 ## - PHYSICAL DESCRIPTION
Extent xiv, 288 pages :
Other physical details illustrations;
Dimensions 24 cm.
505 ## - FORMATTED CONTENTS NOTE
Title <br/>Preface xi PART 1. PRELIMINARIES 1 Chapter 1. Introduction to Probability and Random Variables 3 1.1 Introduction to Random Variables 3 1.1.1 Motivation 3 1.1.2 Definition of a Random Variable and Probability 4 1.1.3 Function of a Random Variable, Expected Value 8 1.1.4 Total Variation Distance 12 1.2 Multiple Random Variables 17 1.2.1 Joint and Marginal Distributions 17 1.2.2 Independence and Conditional Distributions 18 1.2.3 Bayes' Rule 27 1.2.4 MAP and Maximum Likelihood Estimates 29 1.3 Random Variables Assuming Infinitely Many Values 32 1.3.1 Some Preliminaries 32 1.3.2 Markov and Chebycheff Inequalities 35 1.3.3 Hoeffding's Inequality 38 1.3.4 Monte Carlo Simulation 41 1.3.5 Introduction to Cramer's Theorem 43 Chapter 2. Introduction to Information Theory 45 2.1 Convex and Concave Functions 45 2.2 Entropy 52 2.2.1 Definition of Entropy 52 2.2.2 Properties of the Entropy Function 53 2.2.3 Conditional Entropy 54 2.2.4 Uniqueness of the Entropy Function 58 2.3 Relative Entropy and the Kullback-Leibler Divergence 61 Chapter 3. Nonnegative Matrices 71 3.1 Canonical Form for Nonnegative Matrices 71 3.1.1 Basic Version of the Canonical Form 71 3.1.2 Irreducible Matrices 76 3.1.3 Final Version of Canonical Form 78 3.1.4 Irreducibility, Aperiodicity, and Primitivity 80 3.1.5 Canonical Form for Periodic Irreducible Matrices 86 3.2 Perron-Frobenius Theory 89 3.2.1 Perron-Frobenius Theorem for Primitive Matrices 90 3.2.2 Perron-Frobenius Theorem for Irreducible Matrices 95 PART 2. HIDDEN MARKOV PROCESSES 99 Chapter 4. Markov Processes 101 4.1 Basic Definitions 101 4.1.1 The Markov Property and the State Transition Matrix 101 4.1.2 Estimating the State Transition Matrix 107 4.2 Dynamics of Stationary Markov Chains 111 4.2.1 Recurrent and Transient States 111 4.2.2 Hitting Probabilities and Mean Hitting Times 114 4.3 Ergodicity of Markov Chains 122 Chapter 5. Introduction to Large Deviation Theory 129 5.1 Problem Formulation 129 5.2 Large Deviation Property for I.I.D. Samples: Sanov's Theorem 134 5.3 Large Deviation Property for Markov Chains 140 5.3.1 Stationary Distributions 141 5.3.2 Entropy and Relative Entropy Rates 143 5.3.3 The Rate Function for Doubleton Frequencies 148 5.3.4 The Rate Function for Singleton Frequencies 158 Chapter 6. Hidden Markov Processes: Basic Properties 164 6.1 Equivalence of Various Hidden Markov Models 164 6.1.1 Three Different-Looking Models 164 6.1.2 Equivalence between the Three Models 166 6.2 Computation of Likelihoods 169 6.2.1 Computation of Likelihoods of Output Sequences 170 6.2.2 The Viterbi Algorithm 172 6.2.3 The Baum-Welch Algorithm 174 Chapter 7. Hidden Markov Processes: The Complete Realization Problem 177 7.1 Finite Hankel Rank: A Universal Necessary Condition 178 7.2 Nonsuffciency of the Finite Hankel Rank Condition 180 7.3 An Abstract Necessary and Suffcient Condition 190 7.4 Existence of Regular Quasi-Realizations 195 7.5 Spectral Properties of Alpha-Mixing Processes 205 7.6 Ultra-Mixing Processes 207 7.7 A Sufficient Condition for the Existence of HMMs 211 PART 3. APPLICATIONS TO BIOLOGY 223 Chapter 8. Some Applications to Computational Biology 225 8.1 Some Basic Biology 226 8.1.1 The Genome 226 8.1.2 The Genetic Code 232 8.2 Optimal Gapped Sequence Alignment 235 8.2.1 Problem Formulation 236 8.2.2 Solution via Dynamic Programming 237 8.3 Gene Finding 240 8.3.1 Genes and the Gene-Finding Problem 240 8.3.2 The GLIMMER Family of Algorithms 243 8.3.3 The GENSCAN Algorithm 246 8.4 Protein Classification 247 8.4.1 Proteins and the Protein Classification Problem 247 8.4.2 Protein Classification Using Profile Hidden Markov Models 249 Chapter 9. BLAST Theory 255 9.1 BLAST Theory: Statements of Main Results 255 9.1.1 Problem Formulations 255 9.1.2 The Moment Generating Function 257 9.1.3 Statement of Main Results 259 9.1.4 Application of Main Results 263 9.2 BLAST Theory: Proofs of Main Results 264 Bibliography 273 Index 285
520 ## - SUMMARY, ETC.
Summary, etc 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.<br/><br/>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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computational biology.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Markov processes.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Dewey Decimal Classification
Koha item type General Books
100 1# - MAIN ENTRY--PERSONAL NAME
Fuller form of name (Mathukumalli),
Dates associated with a name 1947-
490 0# - SERIES STATEMENT
Series statement Princeton series in applied mathematics
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references (pages 273-283) and index.
906 ## - LOCAL DATA ELEMENT F, LDF (RLIN)
a 7
b cbc
c orignew
d 1
e ecip
f 20
g y-gencatlg
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Collection code Home library Location Shelving location Date of Cataloging Total Checkouts Full call number Barcode Date last seen Price effective from Koha item type
    Dewey Decimal Classification     Non-fiction CUTN Central Library CUTN Central Library Sciences 22/11/2024   570.285 VID 50450 22/11/2024 22/11/2024 General Books