📊 Syllabus

What you will learn

• Bayesian data analysis through probabilistic programming (R/Stan, Python/PyMC, Julia/Turing.jl)¹
• Computational approaches for statistical modeling (quadratic approximation, sampling, MCMC, Hamiltonian Monte Carlo)²
• Causal inference to develop robust statistical models and identify causal relationships
• Machine learning techniques to reduce overfitting in statistical models (e.g., cross-validation, regularization, shrinkage, pooling)

Course overview

This course builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting in today’s model-based statistics, students will perform step-by-step calculations that are usually automated. This unique computational approach ensures that sufficient understanding to make reasonable choices and interpretations in your own modeling work.

We’ll cover causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. If time, we’ll discuss measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding.

The course also includes directed acyclic graph (DAG) approach to causal inference. Additional topics may include the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. Our goal is to go beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.

Course philosophy

Classical statistics classes spend substantial time covering probability theory, null hypothesis testing, and other statistical tests first developed hundreds of years ago. Some classes don’t use software or actual real data and instead live in the world of mathematical proofs. They can be math-heavy and full of often unintuitive concepts and equations.

In this class,³ we will take the opposite approach. We begin with data and learn how to use programming to draw inferences from statistical models.

In other words, there’s way less of this:

\[ Pr(W,L|p) = \dfrac{(W+L)!}{W!L!} p^{W}(1-p)^L \]

And way more of this:

dbinom(6, 9, 0.7)
## [1] 0.27

Over the last decade there has been a revolution in statistical and scientific computing. Open source languages like R and Python have overtaken older (and expensive!) corporate software packages like SAS and SPSS, and there are now thousands of books and blog posts and other online resources with excellent tutorials about how to analyze pretty much any kind of data.

This class will expose you to R—one of the most popular, sought-after, and in-demand statistical programming languages. Armed with the foundation of R skills you’ll learn in this class, you’ll know enough to be able to find how to analyze any sort of data-based question in the future.

Important pep talk!

I promise you can succeed in this class.

Learning Bayesian Statistics and R (or any programming language) can be difficult at first—it’s like learning a new language, just like Spanish, French, or Chinese. Hadley Wickham—the chief data scientist at RStudio and the author of some amazing R packages you’ll be using like ggplot2—made this wise observation:

It’s easy when you start out programming to get really frustrated and think, “Oh it’s me, I’m really stupid,” or, “I’m not made out to program.” But, that is absolutely not the case. Everyone gets frustrated. I still get frustrated occasionally when writing R code. It’s just a natural part of programming. So, it happens to everyone and gets less and less over time. Don’t blame yourself. Just take a break, do something fun, and then come back and try again later. Even experienced programmers and evaluators find themselves bashing their heads against seemingly intractable errors. If you’re finding yourself taking way too long hitting your head against a wall and not understanding, take a break, talk to classmates, e-mail me, etc.

Be confident to be comfortable with confusion

Source: xkcd

Course materials

Course structure

We meet weekly from 12:00-2:45 PM on Mondays in Center City 1101. This course will employ a flipped classroom teaching method.

We will not have lectures during our regularly scheduled class time. Instead, you will do the readings and watch recorded lecture videos prior to each in-person class session. You can do the readings and watch the videos on your own schedule at whatever time works best for you. We will do several things during our Monday in-person classes:

• Extensive Q&A: As you do the readings and watch the videos prior to class, you will inevitably have questions. In your weekly check-in, you can submit (at least) 3 of those questions to me prior to class. We’ll spend a good chunk of each class answering, clarifying, debating, and discussing your questions. We’ll also review the lecture quiz due at the beginning of the class to ensure students are familar with the key concepts of the material

• Activities: In some weeks, we’ll do some in-class activities (labeled as examples) to help solidify concepts about Bayesian statistics, causal inference, and programming. These will not be graded but may aid in upcoming problem set.

• Problem sets: We’ll spend a substantial time during each class learning and working with R together on the problem sets. You’ll need to bring a computer.

Assignments and grades

There are five components to your grade in the course.

1. Participation: Students will receive 5% of their grade based on participation. While I will not actively take attendance, this will be in large part a function of in-class participation (e.g., asking/answering questions, weekly check-ins) as well as out-of-class (e.g., Slack).

2. Lecture quizzes: Before each class (due 11:59am of each class), students will complete a 5 question quiz on the due lecture/chapter. There will be a 10 minute timer and the quizzes will use Canvas. There are no late quizzes that will be accepted as we will review the quizzes first thing for each class. There are eleven (11) total quizzes; however, the two (2) lowest quizzes will be dropped at the end of the semester. Students are not permitted to work with other students on the lecture quizzes.

3. Problem sets: For each lecture, there will be an accompanying problem set. These problem sets will largely mimic those from Richard’s classes with some additional problems. The lowest problem set will be dropped. Problem sets late will receive a 50% reduction. Please take note of the problem set grading rubrics. ⁵

4. Exam: There will be one in-class exam. It will be closed notes and based on chapter lectures, slides, and materials. It will be a blend of multiple choice (very similar to lecture quizzes) and short open ended questions (e.g., reading comprehension or explaining code snippets similar to problem sets).⁶

5. Final Project: The final project will provide students an opportunity to find an application for Bayesian inference. Part of the grade will be two check-in assignments including an in-class presentation on a Bayesian topic and a proposal assignment.

You can find descriptions for all the assignments on the assignments page.