Course Description

This course will provide an introduction to data modeling and Bayesian statistics. Students will learn to develop computer programs to analyze and model data, with an emphasis on ecological and environmental data. We will focus on likelihood and Bayesian approaches to data modeling. Students will use the programming language R (R project website) in an interactive class environment that is based on application, in-class problem solving, and discussions rather than lectures. Class time will consist of discussions and explanation of assigned material driven by student questions (with limited lecturing), reinforced by instructional videos, and in-class exercises that require a laptop computer (please bring a laptop computer to class!). This course is designed to provide students with the analytical tools required for independent research. Students will develop proficiency in utilizing R for data analysis, gain a basic understanding of Bayesian statistics, and become familiar with using Bayesian software packages (Stan, JAGS).

Course Texts and Readings

We will use two books for the class:

Doing Bayesian Data Analysis, 2nd Edition A Tutorial with R, JAGS, and Stan by J. Kruschke.
Introduction to Statistical Thought by Michael Lavine.

Lavine's book can be downloaded for free as a pdf from the link above. Kruschke's book can be purchased at the UVM bookstore.

Please read the assigned chapter prior to coming to class.

We will view online videos and other supplementary material during class time to reinforce concepts.

Computing

Computing is central to this class and we will be doing lots of computer programming. We will have programming exercises in R during class time as well as programming assignments to be completed outside of class. Homework will largely be to develop programs to complete assigned problems. Students need to bring their laptops to class! We will primarily use the programming language R but we may also utilize bits of Python and Mathematica.

I have posted videos detailing the process for installing the R software (below). To obtain R for your own machine, go to the R project website, follow the link beneath 'Download' on the left, choose a site near your geographic location, download the pre-compiled binary distribution for your operating system, and then follow the instructions for installation. After installing R, please install the integrated development environment (IDE) for R called RStudio. Information on downloading and installing RStudio can be found at RStudio.

Grading for Undergraduate students	Grading for Graduate students
In class quizzes on assigned readings: 10% of course grade. Class participation: 10% of course grade. Homework assignments: 60% of course grade. Final exam (take home): 20% of course grade.	In class quizzes on assigned readings: 10% of course grade. Class participation: 10% of course grade. Homework assignments: 50% of course grade. Data analysis project: 10% of course grade. Final exam (take home): 20% of course grade.

Grading for Undergraduate students

Grading for Graduate students

In class quizzes on assigned readings: 10% of course grade.
Class participation: 10% of course grade.
Homework assignments: 60% of course grade.
Final exam (take home): 20% of course grade.

In class quizzes on assigned readings: 10% of course grade.
Class participation: 10% of course grade.
Homework assignments: 50% of course grade.
Data analysis project: 10% of course grade.
Final exam (take home): 20% of course grade.

Schedule*

(K1~Kruschke Chapter 1; L1~Lavine Chapter 1)

Week	Date	Topic	Reading	Exercises	Assignments	Videos & etc
1	Aug	30	Introduction and Background	K2; L Preface	R In Class Exercises Solutions	Kruschke Chapter 2 Solutions	History of R R data types (1) R data types (2)
2	Sep	6	R programming Language	K3	R In Class Exercises Weight data Solutions	Monty Hall problem Monty Hall on Monty Hall Monty Hall background Solution	R data types (3) Subsetting (1) Subsetting (2)
3	Sep	13	Probability	K4; L1.5, 1.6, 1.9		Lavine Exercises Solutions	Vectorization Reading and Writing (1) Reading and Writing (2)
4	Sep	20	Likelihood	L2.3- 2.6		Likelihood Exercises Solutions	Control Structures (1) Control Structures (2) Writing first function
5	Sep	27	Bayes Rule	K5			Functions (1) Functions (2)
6	Oct	4	Binomial Probability	K6,L1.3.1	Function minimization	Likelihood 2 Exercises Solutions Graduate data analysis description due	Scoping rules (1) Scoping rules (2)
7	Oct	11	MCMC	K7.1-7.3			Scoping rules (3) Coding standards
8	Oct	18	MCMC	K7.4-7.6, L6.2	Metropolis MCMC Exercise Solutions		Dates and times
9	Oct	25	MCMC			Normal Regression via MCMC Model template Invgamma Conjugate Prior Solution	lapply apply mapply tapply
10	Nov	1	JAGS	K8	Rjags download Rjags Example		split
11	Nov	8	Stan	K14	RStan Installation 1 RStan Installation 2 RStan Getting Started Stan documentation Stan exercises Stan solution		Debugging (1) Debugging (2) Debugging (3)
12	Nov		GLMs	K15	GLM exercises and HW (due 1 Dec) Solutions		str (2) Simulation (1) Simulation (2)
13	Nov	22	Thanksgiving Break		Thanksgiving Break		Thanksgiving Break
14	Nov	29	Hierarchical Models	K9	JAGS code Data Model structure Solutions		Rprofiler (1) Rprofiler (2)
15	Dec	6	Hierarchical Models	Hierarchical Models Link to book	Owl fecundity diagrams Marina: Meta-Analysis Marina: Plotting function
	Dec	11	Final Exam due by midnight (all) Data analysis project due by midnight (graduate students)	Emailed to me		Final exam

Week

Date

Topic

Reading

Exercises

Assignments

Videos & etc

Aug

Introduction and Background

K2; L Preface

R In Class Exercises
Solutions

Kruschke Chapter 2
Solutions