This page contains links to a text in probabilistic and dynamic programming models for applications to biology. They are made available here free for private study. Otherwise the author reserves copyright privileges. Please send any comments or corrections to ocone@math.rutgers.edu.

1. Chapter 1, Heredity, Genes, and DNA; 25 page pdf file, last revised, January, 2008.

A brief introduction to relevant biological concepts. Contents:

• 1.1 Mendelian Genetics
• 1.2 Genes, Chromosomes and Sexual Reproduction
• 1.3 Genotypes, Phenotypes, and Polymorphisms
• 1.4 Heredity at the Molecular Level
• 1.5 Notes and References

2. Chapter 2, Probability Theory; 38 page pdf file, revised January 2007.

A review of basic probability, with a focus on what is used in the text and examples relevant to biological models.

• 2.1 Probability Spaces
• 2.2 Random Variables
• 2.3 Expectation and Its Application
• 2.4 Central Limit Theorem

3. Chapter 3, Population Genetics Models; 49 page pdf file, revised January, 2008

• 3.1 Introduction
• 3.2 Population Genetics Modeling
• 3.3 One Locus/Two allele Models
• 3.4 Infinite Population Models with Selection
• 3.5 More Problems
• 3.6 Notes and References

4. Chapter 4, Probabilistic Analysis of Sequencing Problems; 45 page pdf file, January 2005. Errata for the posted version of Chapter 4.

• 4.1 Shotgun Sequencing
• 4.2 Restriction Enzyme Digests; Discrete Models
• 4.3 Poisson Random Variables and Poisson Processes

5. Chapter 5, Markov Chain Models; 20 page pdf file, February 8, 2005. Note: At time of posting this chapter is not complete and has not been thoroughly edited. Please inform me of any corrections.

CORRECTION TO PROBLEM 5.4

• 5.1 Introduction
• 5.2 Markov chains; definition
• 5.3 Estimating transition probabilities
• 5.4 Path Probabilities
• 5.5 Problems
• 5.6 Multi-step transition probabilities; Evolution of distributions.
• 5.7 Long-time behavior of Markov chains

6. Chapter 6, Maximum Likelihood Estimation and Hypothesis Testing ; 24 page pdf file, March 27, 2006

Corrections to Chapter 6, April 18, 2005. (These corrections are already made on the version posted March 27, 2006.)

• 6.1 Probability models and hypotheses
• 6.2 Likelihood functions
• 6.3 Maximum Likelihood Estimation
• 6.4 Exercises
• 6.5 Hypothesis testing
• 6.6 Testing independence versus Markov chain dependence in sequence models
• 6.7 Scoring sequenc alignments for homology
• 6.8 Exercises

7. Chapter 7, Sequence Alignment by Dynamic Programming; Sections, 7.1, 7.2.1-7.2.4. 22 page pdf file; Sections 7.2.5--7.2.8 19 page pdf file.

8. Chapter 8, Hidden Markov Models; 26 page pdf file, April 18, 2005.

• 8.1 Definition and basic theory
• 8.2 Graphical representation of hidden chain paths
• 8.3 The forward algorithm
• 8.4 Maximum probability paths
• 8.5 Profile HMM's for protein families