Hidden Markov models for bioinformatics生物信息中隐藏的马可夫模式
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作者： T. Koski 编著
出 版 社： 化学工业出版社
出版时间： 2001-12-1字数：版次： 1页数： 391印刷时间： 2001/12/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9781402001352包装： 精装内容简介
The purpose of this book is to give a thorough and systematic introduction to probabilistic modeling in bioinformatics. The book contains a mathematically strict and extensive presentation of the kind of probabilistic models that have turned out to be useful in genome analysis. Questions of parametric inference, selection between model families, and various architectures are treated. Several examples are given of known architectures (e.g., profile HMM) used in genome analysis.
Audience: This book will be of interest to advanced undergraduate and graduate students with a fairly limited background in probability theory, but otherwise well trained in mathematics and already familiar with at least some of the techniques of algorithmic sequence analysis.
目录
Foreword
1Prerequisites in probability calculus
1.1 Background
1.2 Formulae and Definitions
1.2.1 Alphabet, Sequence
1.2.2 Random Variables and their Distributions
1.2.3 Joint Probability Distributions
1.2.4 Conditional Probability Distributions
1.2.5 A Chain Rule
1.2.6 Independence
1.2.7 Conditional Independence
1.2.8 Probability Models with Independence
1.2.9 Multinomial Probability Distribution
1.2.10A Weight Matrix Model for a Family of Sequences
1.2.11 Simplifying Notations
1.3 Learning and Bayes' Rule
1.3.1 Bayes' Rule
1.3.2 A Missing Information Principle and Inference
1.4 Some Distributions for DNA Analysis
1.4.1 Fragment Accuracy
1.4.2 The Distribution of the Number of Fragments
1.5 Expectation
1.6 Jensen's Inequality
1.7 Conditional Expectation
1.8 Law of Large Numbers
1.9 Exercises
1.10 References and Further Reading:
2 Information and the Kullback Distance
2.1 Introduction
2.2 Mutual Information
2.3 Properties of Mutual Information
2.3.1 Entropy
2.3.2 Some Further Formulas
2.4 Shannon's Source Coding Theorems
2.4.1 AEP
2.4.2 The Source Coding Theorem
2.4.3 Lossless Compression Codes and Entropy
2.5 Kullback Distance
2.5.1 Definition and Examples
2.5.2 Calibration
2.5.3 Properties
2.6 The Score and the Fisher Information
2.7 Exercises on Mutual Information and Codelengths
2.8 Kullback Distance and Fisher Information
2.9 References and Further Reading
3 Probabilistic Models and Learning
3.1 Introduction
3.2 Bayesian probability
3.2.1 Chance and Probability
3.2.2 Coherence
3.3 Models with Conditional Independence
3.3.1 Modelling and Learning for Tosses of a Thumb tack
3.3.2 Learning of the Multinomial Process
3.3.3 General Summary
3.4 Comparison of Model Families
3.4.1 Bayes Factor
3.4.2 Inductive Learning, Updates
3.5 Some Asymptotics for Evidence
3.6 Evidence and Bayesian Codelengths
……
4 EM Algorthm
5 Alignment and Scoring
6 Mixture Models and Profiles
7 Markov Chains
8 Learning of Markov Chains
9 Markovian Models for DNA sequences
10 Hidden Mardov Models: and Overview
11 HMM for DNA Sequences
12 Left to Right HMM for Sequences
13 Derin's Algorithm
14 Forward-Backward Algorithm
15 Baum-Welch Learning Algorthm
16 Limit Points of Baum-Welch
17 Asymptotics of Learning
18 Full probabilistic HMM
Index