Hidden Markov processes: theory and applications to biology
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
2014
|
| Schriftenreihe: | Princeton series in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIV, 287 S. |
| ISBN: | 9780691133157 |
Internformat
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Datensatz im Suchindex
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| adam_text | Hidden Markov Processes
Theory and Applications to Biology
M Vidyasagar
PRINCETON UNIVERSITY PRESS
• PRINCETON AND OXFORD
Contents
Preface
PART 1 PRELIMINARIES 1
Chapter 1 Introduction to Probability and Random Variables 3
1 1 Introduction to Random Variables 3
111 Motivation 3
112 Definition of a Random Variable and Probability 4
113 Function of a Random Variable Expected Value 8
114 Total Variation Distance 12
1 2 Multiple Random Variables 17
121 Joint and Marginal Distributions 17
122 Independence and Conditional Distributions 18
123 Bayes Rule 27
124 MAP and Maximum Likelihood Estimates 29
1 3 Random Variables Assuming Infinitely Many Values 32
131 Some Preliminaries 32
132 Markov and Chebycheff Inequalities 35
133 Hoeffding s Inequality 38
134 Monte Carlo Simulation 41
135 Introduction to Cramer s Theorem 43
Chapter 2 Introduction to Information Theory 45
2 1 Convex and Concave Functions 45
2 2 Entropy 52
221 Definition of Entropy 52
222 Properties of the Entropy Function 53
223 Conditional Entropy 54
224 Uniqueness of the Entropy Function x 58
2 3 Relative Entropy and the Kullback-Leibler Divergence 61
Chapter 3 Nonnegative Matrices 71
3 1 Canonical Form for Nonnegative Matrices 71
311 Basic Version of the Canonical Form 71
312 Irreducible Matrices 76
I313 Final Version of Canonical Form 78
i314 Irreducibility, Aperiodicity, and Primitivity 80
^315 Canonical Form for Periodic Irreducible Matrices 86 t)
viii CONTENTS
3 2 Perron-Frobenius Theory 89
321 Perron-Frobenius Theorem for Primitive Matrices -, 90
322 Perron-Frobenius Theorem for Irreducible Matrices 95
PART 2 HIDDEN MARKOV PROCESSES 99
Chapter 4 Markov Processes 101
4 1 Basic Definitions 101
411 The Markov Property and the State Transition Matrix 101
412 Estimating the State Transition Matrix 107
4 2 Dynamics of Stationary Markov Chains 111
421 Recurrent and Transient States 111
422 Hitting Probabilities and Mean Hitting Times 114
4 3 Ergodicity of Markov Chains 122
Chapter 6 Hidden Markov Processes: Basic Properties 164
6 1 Equivalence of Various Hidden Markov Models 164
611 Three Different-Looking Models 164
612 Equivalence between the Three Models 166
6 2 Computation of Likelihoods 169
621 Computation of Likelihoods of Output Sequences 170
622 The Viterbi Algorithm 172
623 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 Nonsufficiency of the Finite Hankel Rank Condition 180
7 3 An Abstract Necessary and Sufficient 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
77A Sufficient Condition for the Existence of HMMs 211
PART 3 APPLICATIONS TO BIOLOGY 223
I
Chapter 8 Some Applications to Computational Biology 225
841 Some Basic Biology 226
5811 The Genome 226
Chapter 5 Introduction to Large Deviation Theory
5 1 Problem Formulation
5 2 Large Deviation Property for IID Samples: Sanov s Theorem
5 3 Large Deviation Property for Markov Chains
531 Stationary Distributions
532 Entropy and Relative Entropy Rates
533 The Rate Function for Doubleton Frequencies
534 The Rate Function for Singleton Frequencies
CONTENTS I X
812 The Genetic Code 232
8 2 Optimal Gapped Sequence Alignment 235
821 Problem Formulation x ~ 236
822 Solution via Dynamic Programming 237
8 3 Gene Finding 240
831 Genes and the Gene-Finding Problem 240
832 The GLIMMER Family of Algorithms 243
833 The GENSCAN Algorithm 246
8 4 Protein Classification 247
841 Proteins and the Protein Classification Problem 247
842 Protein Classification Using Profile Hidden Markov Models 249
Chapter 9 BLAST Theory 255
9 1 BLAST Theory: Statements of Main Results 255
911 Problem Formulations 255
912 The Moment Generating Function 257
913 Statement of Main Results 259
914 Application of Main Results 263
9 2 BLAST Theory: Proofs of Main Results 264
Bibliography 273
Index 285
|
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| discipline | Biologie Mathematik |
| format | Book |
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| language | English |
| lccn | 014009277 |
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| spelling | Vidyasagar, Mathukumalli 1947- Verfasser (DE-588)124243584 aut Hidden Markov processes theory and applications to biology M. Vidyasagar Princeton, NJ Princeton Univ. Press 2014 XIV, 287 S. txt rdacontent n rdamedia nc rdacarrier Princeton series in applied mathematics Includes bibliographical references and index Computational biology Markov processes Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Hidden-Markov-Modell (DE-588)4352479-5 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Hidden-Markov-Modell (DE-588)4352479-5 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027556587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vidyasagar, Mathukumalli 1947- Hidden Markov processes theory and applications to biology Computational biology Markov processes Markov-Prozess (DE-588)4134948-9 gnd Hidden-Markov-Modell (DE-588)4352479-5 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)4352479-5 |
| title | Hidden Markov processes theory and applications to biology |
| title_auth | Hidden Markov processes theory and applications to biology |
| title_exact_search | Hidden Markov processes theory and applications to biology |
| title_full | Hidden Markov processes theory and applications to biology M. Vidyasagar |
| title_fullStr | Hidden Markov processes theory and applications to biology M. Vidyasagar |
| title_full_unstemmed | Hidden Markov processes theory and applications to biology M. Vidyasagar |
| title_short | Hidden Markov processes |
| title_sort | hidden markov processes theory and applications to biology |
| title_sub | theory and applications to biology |
| topic | Computational biology Markov processes Markov-Prozess (DE-588)4134948-9 gnd Hidden-Markov-Modell (DE-588)4352479-5 gnd |
| topic_facet | Computational biology Markov processes Markov-Prozess Hidden-Markov-Modell |
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