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.

• Prerequisites in probability calculus.
• Information and the Kullback Distance.
• Probabilistic Models and Learning.
• EM Algorithm.
• Alignment and Scoring.
• Mixture Models and Profiles.
• Markov Chains.
• Learning of Markov Chains.
• Markovian Models for DNA sequences.
• Hidden Markov Models: an Overview.
• HMM for DNA Sequences.
• Left to Right HMM for Sequences.
• Derin's Algorithm.
• Forward - Backward Algorithm.
• Baum - Welch Learning Algorithm.
• Limit Points of Baum - Welch.
• Asymptotics of Learning.
• Full Probabilistic HMM.