APM 541 – Stochastic Modeling in Biology
Fall 2013

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 111
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 investigate biological processes. After a brief review of probability theory, we will explore several classes of stochastic models, including discrete and continuous-time 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 model-based statistical analysis of biological data, including Markov-chain Monte Carlo algorithms and approximate Bayesian computation.

Text: Stochastic Modelling for Systems Biology (2nd 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 next-to-last 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 51-61; slides; Oates (2011); Wilson (2013)

27 Aug

Probability: Discrete Distributions

DW 62-76

29 Aug

Probability: Continuous Distributions

DW 77-96

3 Sept

Probability: Limit Theorems

Frank (2009)

5 Sept

Random Number Generation

DW 99-111; slides

10 Sept

Discrete-time Markov Chains: Concepts

DW 123-136; slides

12 Sept

DTMC's: Absorption Probabilities and Times

Caswell (2009)

17 Sept

DTMC's: Stationary Distributions


19 Sept

Population Genetics Models

slides

24 Sept

Population Genetics Models

Patwa & Wahl (2008)

26 Sept

Hidden Markov Models

Gaudart et al. (2009)

1 Oct

Continuous-time Markov Chains: Introduction

DW 137-152; slides

3 Oct

CTMCs: Forward and Backward Equations

Ovaskainen & Meerson (2010)

8 Oct

CTMC's: Construction and Simulation


10 Oct

CTMC's: Asymptotic Behavior

Kar et al. (2009)

15 Oct

Fall Break


17 Oct

Branching Processes

slides; Iwasa et al. (2004)

22 Oct

Genealogies and Coalescents

slides; Hobolth et al. (2007)

24 Oct

Diffusion Processes and Stochastic Calculus

slides; DW 152-164

29 Oct

Diffusion Approximations for Markov Chains

Hu et al. (2012)

31 Oct

Diffusions in Population Genetics

Malaspinas et al. (2012)

5 Nov

Multivariate Diffusions

DW 164-166

7 Nov

Stochastic Simulation: Exact Methods

DW 221-226

12 Nov

Stochastic Simulation: Approximate and Hybrid Methods

DW 226-245; Crudu et al. (2009)

14 Nov

Bayesian Inference

slides; DW 249-254

19 Nov

MCMC: Gibbs Samplers

DW 254-264

21 Nov

MCMC: Metropolis-Hastings Algorithm

DW 264-274; Rasmussen et al. (2011)

26 Nov

Approximate Bayesian Computation

Beaumont (2010)

28 Nov

Thanksgiving Break


3 Dec

Research presentations


5 Dec

Research presentations