APM 541 – Stochastic Modeling in Biology
Fall 2011

Instructor: Dr. Jay Taylor, office: PSA 447; phone: 965-2641; e-mail: jtaylor@math.asu.edu
Time: Tuesdays and Thursdays 12:00-1:15 p.m.
Location: PSA 307
Office Hours: Tuesdays 1:30-3:00 and by appointment.

Course Description: This course will examine some of the ways in which stochastic models are used to analyze biological data, with an emphasis on population genetics, molecular evolution, and epidemiology. After a brief review of probability theory, we will explore several classes of stochastic processes, including discrete and continuous-time Markov chains, diffusion approximations and stochastic differential equations, coalescent processes, and hidden Markov models. Algorithms for simulating these processes will be considered in detail and we will also discuss some of the computational tools that facilitate model-based statistical analyses, such as importance sampling, MCMC, and approximate Bayesian computation.

Text: There is no required text, but a list of books covering some of the topics that we will discuss in class can be found at the following link. There will also be regular reading assignments posted on the syllabus below. Lecture notes, of varying degrees of completeness, can be found here. Optional exercises will also be provided for most of the lectures and you are encouraged (but not required) to attempt these.

Assignments: Each student is expected to complete a research project and to describe their results in a written report and a short oral presentation that will be given at the end of the semester. A short project proposal (1-2 pages) is due on Oct. 11. The projects can be done individually or in pairs and should use probability theory to address a problem in biology. Ideally, these will be related to your dissertation.

Grading: Satisfactory completion of the project will guarantee an A.

Final Exam: Presentations will be held on Wednesday, 8 December 2011 during 9:50 – 11:40 in PSA 307.

Syllabus:

Date

Topic

Readings

18 Aug

Probability: Distributions and Expectation

Charlesworth & Charlesworth (2009)

23 Aug

Probability: Multivariate Distributions


25 Aug

Probability: Approximation and Limit Laws

Frank (2009)

30 Aug

Random Number Generation


1 Sept

Discrete-time Markov Chains: Concepts

Caswell (2009)

6 Sept

DTMC's: Concepts


8 Sept

DTMC's: Absorption Probabilities


13 Sept

DTMC's: Stationary Distributions


15 Sept

The Wright-Fisher and Cannings Models

Der et al. (2011)

20 Sept

Galton-Watson and other Branching Processes

Otto & Whitlock (1997)

22 Sept

Chain Epidemic Models

Longini & Koopman (1982)

27 Sept

Continuous-time Markov Chains: Introduction


29 Sept

CTMCs: Forward and Backward Equations


4 Oct

CTMC's: Construction and Simulation

Gillespie (2001)

6 Oct

CTMC's: Stationary Distributions


11 Oct

CTMC's: Time Reversal

Felsenstein (1981)

13 Oct

Poisson Processes and Random Measures

Rhodes et al. (1996)

18 Oct

Brownian Motion


20 Oct

Diffusion approximation and stochastic calculus

Tuckwell & Williams (2007)

25 Oct

Diffusions in population genetics

Sawyer & Hartl (1992)

27 Oct

Multivariate Diffusions

Innan (2002)

1 Nov

Genealogies and coalescents

Wilson et al. (2005)

3 Nov

Markov Chain Monte Carlo (MCMC): theory

Green (1995)

8 Nov

Bayesian MCMC in population genetics

Drummond et al. (2005)

10 Nov

Ancestral Graphs

McVean & Cardin (2005)

15 Nov

Selective Sweeps and Genetic Hitchhiking

Volkman et al. (2007)

17 Nov

Hidden Markov Models (HMM's)

Gaudart et al. (2009)

22 Nov

Coalescent HMM's

Hobolth et al. (2007)

24 Nov

Thanksgiving break


29 Nov

Approximate Bayesian Computation (ABC)

Beaumont (2010)

1 Dec

Demographic Stochasticity and Antigenic Variation

Minayev & Ferguson (2009)

6 Dec

Molecular Epidemiology

Holmes & Grenfell (2009)