Darryl Holman
117 Denny Hall
206-543-7586
djholman@u.washington.edu
http://faculty.washington.edu/djholman
Winter 2005
Scope: This course will introduce you to the concepts and methods of taking complex real-world systems and creating quantitative models of the system. By the end of the quarter, you will have gained experience in modeling the behavior of a system, developing testable hypotheses, and using observations (taken from fieldwork or data sets) to statistically evaluate hypotheses arising from the model. We will survey some of the concepts, tools, and methods for developing models based on underlying biocultural processes, as well as the methods of testing models from observations collected in anthropological field studies. We will focus on methods for longitudinal research of fertility, mortality, disease dynamics, population genetics, and other biocultural processes, but the concepts and methods are applicable to many other types of anthropological and biocultural research covering the life span.
After a brief introduction to modeling, we will focus on three modeling techniques. (1) We will briefly examine dynamic simulation models. (2) We will spend much time on developing likelihood models. These are models that can be developed from theoretical foundations and can be fit to real data. (3) We will examine simulation models and techniques.
Classes: Monday,
Wednesday and Friday,
Office hours: After
class. Other times can be arranged. You can use email anytime
(djholman@u.washington.edu).
Textbook and readings: There are no required textbooks for this course. I will, however, recommend some of the more important books for this course. Most (if not all) readings will be provided on-line.
Grading: Your course grade will be based on six problem sets (8% each) and a final project (52%).
Problem sets: The six problem sets will consist of several modeling exercises. Frequently, the problems will require the use of computer software. I recommend that you get an account on the CSDE Windows network, as all the required software will be available on those systems. Data sets and other helpful material will be available on the web site. You are free to use books, readings, notes, and web pages to help you work on the problems. You can work in groups, but I recommend you tackle the problems yourselves. Grades for late problem sets will depreciate by 10% per day, including any fraction of a day late. Problem sets are due by the beginning of the class period, one calendar week after being handed out.
There are two software programs we will be using. The first is STELLA, a dynamic modeling and simulation program. A limited version of STELLA is available with one of the optional textbooks or can be downloaded from http://www.hps-inc.com. If you think STELLA will be useful for your research, a full-feature version is available at a substantial student discount from the publisher. One CSDE terminal server has STELLA installed.
The second software package is called mle, and is written by your instructor. You can use this program for maximum likelihood estimation and simulation programming. The software is free from http://faculty.washington.edu/~djholman/mle. Extensive documentation is available online. You can download a pdf version of the documents for browsing or printing. The mle program will also be installed on the CSDE terminal servers. Most of the exercises that use mle can be done in other statistical programming languages (splus, R, Matlab, Gauss, Octave). You are free to use any of these for your work under the idea that learning one such language will help you understand any other. For the statistical programming exercises, mle will be easiest program to use, but other languages (Gauss, R, Matlab) are suitable.
Projects: 52% of your course grade will be based on a project. This project can take one of several forms: (1) a new research proposal in preliminary form incorporating some of modeling ideas covered in the course; (2) a completed existing research or funding proposal (a proposal started in BIO A 525, for example) that is revised to include one or more of the methods covered in this course; (3) a new manuscript in which you have applied methods covered in this course; (4) a term paper in which a model is developed and explored.
Jan 3 Course introduction
Jan 5 Models and the scientific method
Jan 7 Overview of some modeling techniques
Optional
Jan 10 Some useful mathematical tricks (PS 1 assigned)
Jan 12 How to build a model
Jan 14 Dynamic systems models I
Jan 17 No class –
Jan 19 Dynamic systems models II (PS 1 due; PS 2 assigned)
Jan 21 Dynamic systems models III
Optional
Jan 24 Probability models
Jan 26 Likelihood models I (PS 2 due)
Jan 28 Likelihood models II (PS 3 assigned)
Optional
Jan 31 Inference and model selection I
Feb 2 Inference and model selection II
Feb 4 Messy data I (PS 3 due)
Feb 7 Messy data
II (PS 4 assigned)
Feb 9 Heterogeneity I – Measured covariates
Feb 11 Heterogeneity II – Hazard covariate models
Optional
Feb 14 Heterogeneity III – unobserved characteristics (PS 4 due)
Feb 16 Heterogeneity IV – Mixture models
Feb 18 Heterogeneity V – “Sterility” models (PS 5 assigned)
Feb 21 No class –
Feb 23 Convolution models
Feb 25 Clustered observations (PS 5 due)
Feb 28 Heterogeneity VI – time varying covariates
Mar 2 Bootstrapped estimates and other computer intensive methods
Mar 4 Simulation models I (PS 6 assigned)
Mar 7 Simulation models II
Mar 9 Simulation models III
Mar 11 Odds and ends (PS 6 due)
Mar 18 Projects due
by
Bender EA (1978) An Introduction to
Mathematical Modeling.
Cullen MR (1983) Mathematics for the Biosciences.
Simon W (1972) Mathematical Techniques for Biology and Medicine. NY: Academic Press (reprinted by
Thompson Sp and