APM 541 –
Stochastic Modeling in Biology
Fall
2011
Instructor: Dr. Jay Taylor, office: PSA 447; phone:
9652641; email: jtaylor@math.asu.edu
Time: Tuesdays and
Thursdays 12:001:15 p.m.
Location: PSA 307
Office
Hours: Tuesdays 1:303:00 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 continuoustime 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 modelbased 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 (12 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 

23 Aug 
Probability: Multivariate Distributions 

25 Aug 
Probability: Approximation and Limit Laws 

30 Aug 
Random Number Generation 

1 Sept 
Discretetime Markov Chains: Concepts 

6 Sept 
DTMC's: Concepts 

8 Sept 
DTMC's: Absorption Probabilities 

13 Sept 
DTMC's: Stationary Distributions 

15 Sept 
The WrightFisher and Cannings Models 

20 Sept 
GaltonWatson and other Branching Processes 

22 Sept 
Chain Epidemic Models 

27 Sept 
Continuoustime Markov Chains: Introduction 

29 Sept 
CTMCs: Forward and Backward Equations 

4 Oct 
CTMC's: Construction and Simulation 

6 Oct 
CTMC's: Stationary Distributions 

11 Oct 
CTMC's: Time Reversal 

13 Oct 
Poisson Processes and Random Measures 

18 Oct 
Brownian Motion 

20 Oct 
Diffusion approximation and stochastic calculus 

25 Oct 
Diffusions in population genetics 

27 Oct 
Multivariate Diffusions 

1 Nov 
Genealogies and coalescents 

3 Nov 
Markov Chain Monte Carlo (MCMC): theory 

8 Nov 
Bayesian MCMC in population genetics 

10 Nov 
Ancestral Graphs 

15 Nov 
Selective Sweeps and Genetic Hitchhiking 

17 Nov 
Hidden Markov Models (HMM's) 

22 Nov 
Coalescent HMM's 

24 Nov 
Thanksgiving break 

29 Nov 
Approximate Bayesian Computation (ABC) 

1 Dec 
Demographic Stochasticity and Antigenic Variation 

6 Dec 
Molecular Epidemiology 