QERM 598: Computational Methods in Quantitative Ecology

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Mosaic plot of Steller sea lion birth probabilities
  • This course is designed to introduce students to computational methods in Ecological Modeling. Commonly used techniques in Applied Statistics will be covered, as well as some deterministic and stochastic models encountered in Mathematical Biology. While we cover the mechanics of doing various statistical analyses, the goal of the course is to develop the ability to use computational tools creatively to help visualize and grasp statistical concepts and modeled processes. There will be lots of emphasis on simulation and graphical visualization, since these are such an important tools in practice but scantily touched upon in other courses.
  • Our primary tool will be R.
  • Each week will consist of a lecture, an R lab and an assignment. One of the practical goals is to create a body of labs, assignments and datasets that can be used as a basis for a continuation of this course in years to come. All of these materials will be stored on this website.


Contents

Practical Details

  • Location: Odegaard Undergraduate Library Computer Lab 102
  • Times: Wednesday - 1:30-3:30
  • Instructor: Eli Gurarie with the possible participation of guest lecturers, under the benevolent auspices of Dr. Tilmann Gneiting.
  • Office Hours: all day Wednesday in Loew 328 and by appointment.
  • Target Audience: First-year QERM students and other qualified students interested in Quantitative Ecology.
  • Prerequisites: Statistical Inference (STAT 512), Mathematical biology (AMATH 420)


Week by Week: Homeworks, Labs, Data and Notes for QERM 598

Box-plots


Week 0: Basic Introduction to R

If you don't have R already, you can download it from this website. You'll need to download the executable binaries: For Windows users they are here; for MacOS users they are here. Install R and run it.

R is an open source program, which means it's free, efficient and no-frills. It also means that documentation is patchy at best and learning how to use it involves poking around the internet, blindly groping around the internal help file, and, whenever possible, stealing other people's code.

Thankfully, there is lots of expertise at QERM! To start off, download or open the file below, print it out, read it, and walk through the examples. There is a brief assignment at the end of the lab for practice.


Week 1: Distributions and the Central Limit Theorem

Obtaining quantiles and p-values from distributions. Plotting cdfs and pdfs. Generating random data. Introducing plotting functions and loops. Illustrating the Central Limit Theorem numerically.


Week 2: Comparing two samples: Monte Carlo and t-tests

You will need to download the following data files to perform the lab and the homeworks:

You will also need to read Mike Keim's Pdf10.png notes on non-parametric tests.


Week 3: Introduction to Analysis of Variance


Week 4: Linear Regression


Week 5: Chi-squared Contingency Tables

There is, by the way, a great explanation/derivation of the theory behind Chi-Squared contingency tests and other applications of the central limit theorem here.

Also, visit this link on making mosaic plots of categorical data: R tips/Contingency Tables.


Week 6: Introduction to Stochastic Modelling


Week 7: Population Dynamics Models and MCMC


Week 8: Project Discussions


Week 9: Fitting models and optimization


Week 10: Final project presentations
  • Please visit the Final Projects page to browse through final project presentations and R code.
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