This page contains links to a text in probabilistic and dynamic programming models for applications to biology.

Readers are invited to 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: Difference Equation Models; 48 page pdf file, revised January, 2009 (NOTE to Spring 2009 students: make sure you have this version!)

• 3.1 Finite Difference Equations
• 3.2 Modeling principles for population genetics
• 3.3 Models with no selection
• 3.4 An infinite population models with selection
• 3.5 Notes and References

4. New chapter 4, Markov Chains and Applications to Population Genetics;

• 4.1 Introduction
• 4.2 Markov chains; introduction
• 4.3 Analysis of Markov chains and applications
• 4.4 Recurrent chains

5. Chapter 5, Probabilistic Analysis of Sequencing Problems; 45 page pdf file, January 2009. (Old Chapter 4, relabeled as Chapter 5)

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

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