Instructor:
Michael C. Dietze
STO 457A
Office hours by appointment
Goals:
The primary focus of this course is on probabilitybased statistical methods employed in the environmental, earth, and ecological sciences. Students in this class will explore a variety of statistical modeling topics from both a likelihood and Bayesian perspective, building progressively from simple models to sophisticated analyses. Students will be exposed to the concepts behind these approaches, the computational techniques to implement them, and their application to common problems in environmental science.Throughout the focus will be on how to construct statistical models that allow us to confront theory with data. The first third of the course will cover foundational concepts. The middle third will work from simple linear regression up to general linear mixed models and hierarchical models with particular emphasis on the complexities common to environmental data: heteroskedasticity, missing data, latent variables, errors in variables, and multiple sources of variability at different spatial,temporal, and taxonomic scales. The last third will cover timeseries and spatial data, both of which are ubiquitous in the environmental and earth sciences. Attention throughout the course will be given to environmental applications, and in particular data and models unique (e.g. markrecapture, matrix population models) or particularly important (e.g. kriging, CAR) to earth and environmental science.
Contact hours/week: Three 50min lectures and one 2hr computer lab
Prerequisites:
Introductory statistics (CAS MA115/116 or MA213/124 or equivalent) and
Calculus I (CAS MA121 or CAS MA123 or equivalent) and
Probability(CAS MA581) or consent of the instructor
BU HUB:
This course meets the following HUB learning outcomes
Philosophical Inquiry and Life’s Meanings
1. Students will demonstrate knowledge of notable works in philosophical thought, make meaningful connections among them, and be able to relate those works to their own lives and those of others.
This course makes important connections between the philosophy of science and the practical applications of statistical methods. We explicitly discuss multiple alternative schools of thought in the philosophy of science (Popper, Kuhn, Polanyi, Lakotos) and how they relate to hypothesis testing and model selection. A core, recurring component of the course involves an ongoing discussion about Bayesian vs. frequentist philosophies: What do probability and uncertainty mean (e.g. is probability subjective or objective)? How does the fact that we can never observe the world perfectly affect our ability to make inferences? Is there chance/stochasticity in the world around us, or is the universe fundamentally deterministic, and how does that belief affect our ability to make inferences about the world around us? How do these philosophies impact the types of questions we can ask about the natural world? Students will demonstrate this knowledge through a combination of exam questions and lab reports.
2. Students will demonstrate the reasoning skills and possess the vocabulary to reflect upon significant philosophical questions and topics such as what constitutes a good life, right action, meaningful activity, knowledge, truth, or a just society.
As noted in Outcome 1, this course will ask students to reflect on significant questions about knowledge and truth. Demonstration of vocabulary, reasoning skills, and notable works will occur through exam questions and lab report questions.
Writing Intensive
1. Students will be able to craft responsible, considered, and wellstructured written arguments, using media and modes of expression appropriate to the situation.
The semester project is a core component of this course, which culminates in a 5000 word paper (1520 pages double spaced, plus abstract, figures, tables, and citations) written according to the guidelines and style of a scientific journal. The development of the paper is scaffolded through a number of project milestones where students get feedback from the instructor and have the opportunity to revise the different sections of the paper (project prospectus = Introduction, model description = Methods, preliminary results = Results). There is also one lab (#12) specifically set aside for paired reviews, where students receive both oral and written feedback from a peer. In addition, students will also submit thirteen other lab reports, with a typical length of 1025 pages each (including text, code, figures, and tables). Aimed at graduate student and upperlevel undergraduates in our major, learning wellstructured scientific writing is the key mode of expression appropriate for this discipline.
2. Students will be able to read with understanding, engagement, appreciation, and critical judgment.
In addition to technical writing, this course will help students to better develop skills at technical reading. Indeed, a core aim of this course is to enable students to be able to read and critically evaluate the modern quantitative methods used in the primary scientific literature. Specifically, through the use of casestudy based labs students will learn how to evaluate the hypotheses laid out in each problem, the statistical models used to test these hypotheses, and the results and discussion of such models.
3. Students will be able to write clearly and coherently in a range of genres and styles, integrating graphic and multimedia elements as appropriate.
Students will integrate graphic elements (figures and graphs) throughout their lab reports and final project.
Course Materials:
Required Text: Models for Ecological Data: An Introduction. 2007. James S. Clark ISBN: 9780691121789
Book is available at the university bookstore or can be purchased online
The primary text will be supplemented with PDFs of select readings from additional textbooks and the primary literature. Literature readings focus on examples of the application of statistical models in the environmental literature rather than methods papers. These “case studies” will also serve as the focus for the analysis problems in the lab component.
Students will also make extensive use of the following statistical software (which is freely available on the internet) in order to complete assignments:
If you want to avoid running computationallyintensive analyses on your personal computer / laptop, you may want to try running RStudio Server through the SCC OnDemand web interface, which will allow you to run jobs on BU SCC cluster (BU only)
Grading:
Grading will be based on lab reports/problem sets, a semesterlong project, and four exams.
Lab reports/problem sets (10 points each)  = 130 
Semester project  = 80 
project proposal (10)  
model description (10)  
preliminary analysis (20)  
final report (40)  
Exams (20, 20, 25, 25 points )  = 90 
Total  = 360 
Lectures/Labs
Please refer to the course website for the schedule of lecture/lab topics and the assigned readings that go with these. Students are expected to complete readings before class.
Lab attendance is mandatory. Lab reports will not be accepted for labs missed due to unexcused absences. Lab reports are due by the start of lab the following week and will be penalized 10%/day if turned in late. Lab materials will be made available in the GitHub repository. Details on what needs to be turned in will be provided with each lab.
You may discuss lab assignments with other students, but you each must turn in your own written report and code.
Semester Project
A core component of this course is a semesterlong independent analysis and writeup. There are a number of benchmarks over the course of the semester to ensure adequate progress is being made and to provide you with feedback. A more detailed description will be provided before each task is due.
Project Proposal: 12 pages doublespaced. Students are expected to describe the data set they intend to analyze and present the scientific question that motivates their analysis. Students are encouraged to make use of their own data sets for the semester project.
Model description: 12 pages doublespaced. A brief description of how the data will be analyzed. Should include a mathematical specification of the process model(s), the data model, and the parameter model and a figure of how these relate to one another.
Preliminary Analysis: 13 pages double space text plus R/BUGS code plus a minimum of 5 results figures with legends. At this point analysis should be mostly complete. Text should briefly describe the computational methods of the analysis and any modifications of the model description (i.e. what did you actually end up doing).
Final Report: The final report should be written in the style and tone of a scholarly publication, though with greater emphasis on the results and statistical methods employed and less on introduction and discussion. Specifically, we will be using the Ecology Letters format: no more than 5000 words in length and no more than 6 figures or tables. For more detailed guidelines see http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%2914610248/homepage/ForAuthors.html
Project Due Dates:
Project Proposal: 2/11
Model Description: 3/14
Preliminary Analysis: 4/22
Final Report: Before Exam 4 (Final)
Exams
Exams will be a combination of short answer and multiple choice. The final exam will be noncumulative.
Midterm I: 2/7
Midterm II: 2/22
Midterm III: 4/1
Final: 5/10
Lecture Schedule
Date 
Topics 
Reading 
Project 
1/21 
Introduction to modelbased inference 
Clark: Chapter 1 

1/24 
Probability theory: joint, conditional, and marginal distributions 
Hilborn and Mangel Ch 3 p3962 

1/26 
Probability theory: discrete and continuous distributions 
Hilborn and Mangle Ch 3 p6293 

1/28 
Maximum Likelihood 
Chapter 3.13.2 

1/31 
Point estimation by MLE 
Chapter 3.33.5 

2/2 
Analytically tractable MLEs 

2/4 
Intractable MLEs and basic numerical optimization 
Chapter 3.103.13 

2/7 
EXAM 1: Probability Theory, Maximum Likelihood 

2/9 
Bayes Theorem 
Chapter 4.1 

2/11 
Point estimation using Bayes 
Chapter 4.2 

2/14 
Analyticallytractable Bayes: conjugacy and priors 
Chapter 4.3, Appendix G 

2/16 
Numerical methods for Bayes: MCMC 
Chapter 7.17.2, 7.3 intro 

2/18 
MCMC: MetropolisHastings, Gibbs 
7.3.17.3.4, 7.5 

2/22 
EXAM 2: Bayes, MCMC 

2/23 
Interval Estimation: Bayesian credible intervals 
Chapter 5 

2/25 
Frequentist confidence intervals I: Likelihood profile, Fisher information 
Chapter 5 

2/28 
Frequentist confidence intervals II: Bootstrapping 
Chapter 5 

3/2 
Hypothesis testing & competing philosophies of science: Popper, Kuhn, Polanyi, & Lakotos 
Hilborn and Mangel Chapter 2 

3/4 
Model Selection: Likelihood ratio test, AIC, DIC, predictive loss, model averaging 
Hilborn and Mangel Chapter 2 

SPRING BREAK 

3/14 
Heteroskedasticity, Missing data models 
Chapter 5.4 & 7.4 
Model Description 
3/16 
Errors in variables, Latent variables, Philosophy of science: imperfect observation 
Chapter 7.6, 7.7, 8.1 

3/18 
Logistic regression 
Chapter 8.28.2.3 

3/21 
GLMs 
Chapter 8.28.2.3 

3/23 
Hierarchial Bayes 
Chapter 8.2.4 

3/25 
Hierarchical Bayes 2 
Chapter 8.2.5  8.3 

3/28 
GAMs and basis functions 
Slides 

3/30 
TBD 

4/1 
EXAM 3 GLMM, HB 

4/4 
Hierarchical Bayes 
Chapter 8.2.58.3  
4/6 
Nonlinear models 
Chapter 8.4 

4/8 
Applications of random effects models 
Chapter 8.58.7 

4/11 
Time series: Basics and StateSpace 
Chapters 9.1, 9.2, 9.6 

4/13 
Time series: MarkRecapture 
Chapter 9.7, 9.8, 9.16 

4/15 
Time series: ARMA 
Chapter 9.3, 9.5 

4/18 
Patriot's Day, No Class 

4/20 
Time Series: Repeated Measures 
Chapter 9.10, 9.14, 9.15 

4/22 
Spatial: pointreferenced (geostatistical) data & Kriging 
Chapter 10.7 
Preliminary Analysis 
4/25 
Spatial: Markov Random Field 
Chapter 10.8 

4/27 
Spatial Basis functions 

4/29 
Spatial: blockreferenced data and misalignment 
Chapter 10.9 

5/1 
Spatial: conditional autoregressive models (CAR) 
Chapter 10.10 

5/4 
TBD 

5/10 
EXAM 4, 911AM 
Lab Syllabus
Lab 
Week 
Topics 
Software 
1 
1/26 
Introduction to R 
R 
2 
2/2  Probability distributions and sampling 
R 
3 
2/9 
Fire return intervals: Maximum likelihood basics 
R 
4 
2/16 
Ecosystem responses to CO2: ML numerical optimization 
R 
5 
2/23 
Forest stand characteristics: Intro to BUGS 
JAGS 
6 
3/2 
Regression: Gibbs sampler 
R 
7 
3/16 
Nonlinear plant growth: Metropolis Algorithm 
R 
8 
3/23 
CO2 revisited: Interval estimation and model selection 
R 
9 
3/30 
Understory Regeneration: Random effects 
Both 
10 
4/6 
Mosquito abundance: Hierarchical modeling 
JAGS 
11 
4/13 
Moose population fluctuations: Statespace time series 
JAGS 
4/20 
Wed = Mon; no lab 

12 
4/27 
Peer Assessment of projects 

13  5/4 
Ozone: Space/time exploratory data analysis 
R 
Academic Code
It is your responsibility to know and understand the provisions of the CAS Academic Conduct Code. Copies are available in CAS 105. Suspected cases of academic misconduct will be referred to the Dean’s Office. See http://www.bu.edu/academics/resources/academicconductcode for conduct information for undergraduates and http://www.bu.edu/cas/students/graduate/formspoliciesprocedures/academicdisciplineprocedures/ for graduate student conduct requirements.