Content
This course is an introduction to the modern theory and practice of scientific data analysis using both classical and modern approaches. The unifying concepts are those of probability model, information, and inference. Students will learn and use the basic principles of model formulation, estimation, interpretation, criticism, and refinement. The course will make use of lectures, readings, and computer exercises in the R statistical computing environment. Students will obtain hands-on experience in data analysis using data provided by the instructor and students. In particular, students with scientific questions of their own and data sets to analyze will have a chance to work on these in the course. Students will develop and practice good habits in the organization, performance, and presentation of data and data analysis. Although examples will be for the most part drawn from Ecology, students from other disciplines, including Evolutionary Biology, Public Health, and Natural Resources, will learn valuable technique.
Topics
- exploratory data analysis
- data visualization
- literate programming
- reproducible research
- review of probability
- theory of scientific inference
- general linear models
- nonlinear models
- generalized linear models
- stochastic simulation
- likelihood
- maximum-likelihood inference
- Bayesian inference
- hierarchical/mixed-effects models
- dynamic models
Additional topics that may be covered, if there is opportunity and interest, include
- phylogenetic comparative analysis
- the bootstrap and other resampling schemes
- spatial models
Audience
The course is suitable for theoretically and mathematically-minded science and engineering students. Applied mathematicians, statisticians, computer scientists, and engineers are especially welcome, as are students of biology, ecology, evolution, epidemiology, environmental sustainability, economics, social sciences, and bioinformatics with suitable mathematical backgrounds.
Objectives
Students completing the course will have gained
- facility with the statistical analyses most commonly needed in ecology,
- good habits of data organization, visualization, and analysis, which will facilitate their ability to perform sound, transparent, and reproducible research,
- a deep understanding of the fundamental theory of statistical inference, which will allow the design of new analyses customized to specific questions and data, and
- the background needed to understand and criticize models and statistical inference in the scientific literature.
Prerequisites
Students are expected to have an undergraduate-level grounding in calculus and statistics. Students unfamiliar with numerical computation in any language on any platform should consult with the instructor before registering for the course.
Work required
You must attend lectures and complete the assigned homework exercises, which will be collected & graded. We will regularly work on these in class.
Writing
Because logical reasoning is an essentially linguistic activity, a subsidiary but very important aim of the course is to improve your mathematical writing ability. Feedback on your written work will be aimed at bringing your reasoning and writing to a high standard of excellence. The following guidelines are provided to assist you in achieving this goal:
- Make each submission self-contained. It should be possible for someone to pick up, read, and understand your submission without having to find and read any other document. This will make your written work a more valuable supplement to your notes, as you will be able to read and understand it years hence.
- Never turn in a rough draft. It will typically be necessary to write at least one rough draft before preparing a final copy for submission. Scratch work, notes to self, dead ends, and minor calculations, such as are found in a rough draft, do not belong on the final copy.
- Write for your peers. The final copy may end up being substantially more concise than the rough draft. For example, though there is no single standard, it is generally not necessary to include every step of a computation or argument in the final copy. A good guideline is to write not for the professor but rather for an audience composed of your peers, with similar background, preparation, and skill level. Not only is this an intuitive guideline to follow, doing so will increase the value of your written work as a supplement to your notes.
You will not be expected to reach this standard immediately. Rather, expect constructive criticism about not only the content, but also the style, of your written work. As the course progresses, you will be expected to incorporate these lessons into your writing.
Bookshelf
The following are some reference materials that you may find useful.
- R: The Big Book of R. A one-stop shop with links to all sorts of web resources on the R computing environment.
- Linear algebra: Strang, Gilbert. Linear algebra and its applications Thomson, Brooks/Cole, 2006. An excellent introduction to applications.
- Applied mathematics: Strang, G. Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986. A treasury of applied mathematics technique.
- Differential equations: Hirsch, M. W. & Smale, S. Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, 1974. An excellent mathematical introduction to the subject.
- Differential equations, Strang, G. Differential equations and linear algebra. Wellesley-Cambridge Press, 2014. Haven’t read this, but if it’s as good as his other books, it will be excellent.
- Prof. Strang also has an excellent series of lectures available for streaming through Open Courseware and YouTube.
- Differential equations, Arnol’d, V. I. Ordinary Differential Equations. MIT Press, 1973. A high-level perspective from one of the great dynamical systems theorists.
- Probability: Grimmett, G. & Stirzaker, D. Probability and random processes. Oxford University Press, 2001.
- Probability: Feller, W. An introduction to probability theory and its applications. Wiley, 1968. The classic two-volume reference.
- Stochastic processes: Gardiner, C. Stochastic Methods. Springer, 2009.
- Mathematical biology:, Ellner, S. P. & Guckenheimer, J. Dynamic Models in Biology. Princeton University Press, 2006. Introduction to biological dynamics.
- Mathematical ecology, including demography and some eco-economics: Kot, M. Elements of Mathematical Ecology. Cambridge University Press, 2001.
- Calculus for biologists: Garfinkel, A., Shevtsov, J. & Guo, Y. Modeling life : the mathematics of biological systems. Springer, 2017. A very good lower-division introduction to calculus in the life sciences. A PDF is available on the course Dropbox.
- Matrix models: Caswell, H. Matrix Population Models. Sinauer, 2001. The definitive text on these versatile models.
- Population dynamics: Turchin, P. Complex Population Dynamics: A Theoretical/Empirical Synthesis. Princeton University Press, 2003.
- Evolutionary game theory: Hofbauer, J. & Sigmund, K. Evolutionary Games and Population Dynamics. Cambridge University Press, 1998.
Course policies
Academic integrity
The University of Michigan community functions best when its members treat one another with honesty, fairness, respect, and trust. The college promotes the assumption of personal responsibility and integrity, and prohibits all forms of academic dishonesty and misconduct. All cases of academic misconduct will be referred to the LSA Office of the Assistant Dean for Undergraduate Education. Being found responsible for academic misconduct will usually result in a grade sanction, in addition to any sanction from the college. For more information, including examples of behaviors that are considered academic misconduct and potential sanctions, please see lsa.umich.edu/lsa/academics/academic-integrity.html.
Course Recordings
Students are prohibited from recording/distributing any class activity without written permission from the instructor, except as necessary as part of approved accommodations for students with disabilities. Approved recordings will be only for the student’s own private use.
Incompletion
Students in good standing (i.e., grade of B or better), forced by circumstances beyond their control to withdraw entirely from school after the withdrawal deadline may request a grade of Incomplete. The instructor may request proof of the necessitating circumstances and will, in consultation with the student, set the terms for the timely completion of course requirements.
Disability Statement
The University of Michigan is committed to providing equal opportunity for participation in all classes, programs, services and activities. Requests for accommodations by persons with disabilities may be made by contacting the Services for Students with Disabilities (SSD) Office located at G664 Haven Hall. The SSD phone number is 734-763-3000. Once your eligibility for an accommodation has been determined you will be issued a verified individual services accommodation (VISA) form. Please present this form to me at the beginning of the term, or at least two weeks prior to the need for the accommodation (i.e., examination).
Mental Health and Well-Being
University Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressures and challenges associated with relationships, mental health, alcohol or other drugs, identities, finances, etc. If you are experiencing concerns, seeking help is a courageous thing to do for yourself and those who care about you. If the source of your stressors is academic, please contact me so that we can find solutions together. For personal concerns, U-M offers a variety of resources, many which are listed on the Student Well-being webpage.
Sexual Misconduct Policy
Title IX prohibits discrimination on the basis of sex, which includes sexual misconduct—including harassment, domestic and dating violence, sexual assault, and stalking. I understand that sexual violence can undermine your academic success, so I encourage anyone dealing with sexual misconduct to talk to someone about their experience, so they can get the support they need. Confidential support and academic advocacy can be found with the Sexual Assault Prevention and Awareness Center (SAPAC) on their 24-hour crisis line, 734.936.3333 and at sapac.umich.edu.
Violations can be non-confidentially reported to the Office for Institutional Equity (OIE) at institutional.equity@umich.edu.