APM 541 –
Stochastic Modeling in Biology
Fall
2013
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 111
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 investigate biological processes. After a brief review of probability theory, we will explore several classes of stochastic models, including discrete and continuoustime Markov chains, branching processes, coalescents, Hidden Markov models, and diffusion approximations and stochastic differential equations. Examples of biological applications will be taken from population genetics and evolutionary biology, population ecology, epidemiology, cell biology and gene regulatory networks. Particular emphasis will be placed on stochastic simulation and on modelbased statistical analysis of biological data, including Markovchain Monte Carlo algorithms and approximate Bayesian computation.
Text: Stochastic Modelling for Systems Biology (2^{nd} edition) by Darren Wilkinson. This will be supplemented by readings from the primary literature, which will be posted on the syllabus below. Lecture notes, of varying degrees of completeness, will be made available here.
Assignments: Class participants will be expected to complete a research project that investigates a stochastic model of some biological process and to present their results in a written report and in a short oral presentation. A short project proposal (1 page) is due on Oct. 8. Group projects will require instructor approval. Presentations will take place during the last week of class and during the final exam period (TBA). The written reports will be due on the nexttolast day of class (Dec 3) and each report will be read and marked by the instructor and three members of the class. Peer reviews will be due during the final exam period.
Grading: Satisfactory completion of the project will guarantee an A.
Syllabus:
Date 
Topic 
Readings 
22 Aug 
Probability: Introduction 
DW 5161; slides; Oates (2011); Wilson (2013) 
27 Aug 
Probability: Discrete Distributions 
DW 6276 
29 Aug 
Probability: Continuous Distributions 
DW 7796 
3 Sept 
Probability: Limit Theorems 

5 Sept 
Random Number Generation 
DW 99111; slides 
10 Sept 
Discretetime Markov Chains: Concepts 
DW 123136; slides 
12 Sept 
DTMC's: Absorption Probabilities and Times 

17 Sept 
DTMC's: Stationary Distributions 

19 Sept 
Population Genetics Models 

24 Sept 
Population Genetics Models 

26 Sept 
Hidden Markov Models 

1 Oct 
Continuoustime Markov Chains: Introduction 
DW 137152; slides 
3 Oct 
CTMCs: Forward and Backward Equations 

8 Oct 
CTMC's: Construction and Simulation 

10 Oct 
CTMC's: Asymptotic Behavior 

15 Oct 
Fall Break 

17 Oct 
Branching Processes 

22 Oct 
Genealogies and Coalescents 

24 Oct 
Diffusion Processes and Stochastic Calculus 
slides; DW 152164 
29 Oct 
Diffusion Approximations for Markov Chains 

31 Oct 
Diffusions in Population Genetics 

5 Nov 
Multivariate Diffusions 
DW 164166 
7 Nov 
Stochastic Simulation: Exact Methods 
DW 221226 
12 Nov 
Stochastic Simulation: Approximate and Hybrid Methods 
DW 226245; Crudu et al. (2009) 
14 Nov 
Bayesian Inference 
slides; DW 249254 
19 Nov 
MCMC: Gibbs Samplers 
DW 254264 
21 Nov 
MCMC: MetropolisHastings Algorithm 
DW 264274; Rasmussen et al. (2011) 
26 Nov 
Approximate Bayesian Computation 

28 Nov 
Thanksgiving Break 

3 Dec 
Research presentations 

5 Dec 
Research presentations 
