Environmental Data Analysis and Modeling
Environmental data are messy in specific, structured ways: observations are correlated in space, they drift and jump in time, and the interesting signal is usually the trend rather than the mean. This course teaches the statistical and machine learning methods that handle those properties, and teaches them as ideas rather than as a catalogue of routines.
The emphasis throughout is on conceptual understanding. Students learn not only how to fit a model but how to check it, how to choose between models, and how to articulate what a model cannot tell them. Every method is paired with an in-class coding exercise on a real environmental dataset.
What you will learn
- How to think about statistical data and their analysis in the context of typical environmental problems
- Key techniques in statistical modeling and machine learning, their underlying ideas, where they apply, and how to use them
- How to build, select, and check statistical models using modern computational techniques
- How to address the core challenges of environmental data: spatial correlation, structured time-series behavior, changepoints, and trends
Above all, students learn to think critically about environmental data and models, and to discuss the limitations of the models they encounter in the wild.
Topics
Foundations. Model estimation, multivariate distributions, exploratory analysis and visualization of environmental data.
Regression. Simple and multiple linear regression, weighted least squares, and diagnostics.
Trends and change detection. Autoregressive models, rank-sum tests, t-tests and the bootstrap, and the Mann-Kendall test for monotonic trend.
Flexible and generalized models. Local regression, generalized linear models.
Dimension reduction and learning. LASSO and principal component analysis, classification with support vector machines, and clustering.
Ensemble and neural methods. Boosting and XGBoost; neural networks through to large language models, and what they do and do not add over the classical toolkit.
Spatial statistics. Trend surface estimation, variograms, and kriging, including its relationship to Gaussian process regression.
Computing
All computation is done in R using Jupyter notebooks, leaning on the tidyverse package ecosystem. Prior R experience is not expected; the first assignment is a guided R tutorial. The choice of R is deliberate: the breadth of statistical methods already implemented, and the readability of tidyverse code, give students the most leverage for the time invested.
Each topic comes with an in-class notebook exercise worked through together, covering datasets such as global temperature records, air quality measurements, aquifer surveys, and New York City electricity demand and prices.
Prerequisites
A prior statistics course (STAT 4001, IEOR 3658, or IEOR 4150) and basic programming background (ENGI 1006). Matrix and vector algebra, discrete and continuous probability distributions, sample estimates, correlation and covariance are assumed and are not re-taught. A diagnostic assignment is posted before the first class so students can assess their own background.
Assessment
Computational homework carries most of the grade, with two short in-class quizzes and participation making up the remainder. Homework is submitted as a Jupyter notebook together with its rendered output; students are asked to explain how they arrived at each solution, not only to report it.
Use of AI tools
Students may use large language models and coding assistants to help with syntax, debugging, and exploring alternative approaches. The standard is that students remain fully responsible for everything they submit: they must understand, verify, and be able to defend any code, result, or explanation they hand in. Submitting unverified AI output is treated as academic misconduct.
Reference textbooks
- James, Witten, Hastie, and Tibshirani, An Introduction to Statistical Learning (freely available)
- Helsel and Hirsch, Statistical Methods in Water Resources, U.S. Geological Survey (freely available)
- Hengl, A Practical Guide to Geostatistical Mapping (freely available)