PSY9550 – Statistical thinking and Bayesian Data analysis
Schedule, syllabus and examination date
Course content
Statistical analysis is often pursued with the goal of obtaining statistically significant results. The book “Statistical Rethinking” offers an alternative approach, where the goal is to faithfully model the data based on domain knowledge and then draw inferences. Faithful modeling of data requires exploring and comparing statistical models (including the generalized linear model) of different complexities. Hence, the course will introduce Bayesian inference, which reliably fits statistical models, and model comparison. An important part of the domain knowledge that influences how data should be analyzed are the (assumed) causal relationships of observed or measured variables. Therefore, the course also introduces directed acyclic graphs as a method to describe and examine domain knowledge.
The course will be organized around reading the Book “Statistical Rethinking” (https://xcelab.net/rm/statistical-rethinking/) and solving exercises in the programming language R.
Learning outcome
Knowledge:
- Understanding the difference between data generating processes and statistical models
- Bayesian statistics
- Directed acyclic graphs and causal inference
- Model comparison (and selection)
- Generalized linear model
- Hierarchical (multilevel) models
Skills:
- Understand and formulate simple and complex regression models (also in the R package “brms”) including correct choice of covariates.
- An important goal of the seminar is to learn to learn. That is, that students become confident that they can learn new methodological skills on their own when needed.
Prerequisites
Formal prerequisite knowledge
Basic familiarity with R. The R code used in the seminar is simple.
Teaching
There will be no lectures or longer presentations in the seminar. Everyone is asked to read assigned chapters (there are also online lectures, which are not a supplement for reading) and to solve the exercises for a chapter before the seminar. In addition to reading the assigned chapters, one can also watch accompanying videos on YouTube: https://www.youtube.com/playlist?list=PLDcUM9US4XdMROZ57-OIRtIK0aOynbgZN.
It is important to emphasize that reading the chapters and doing exercises are central to the course and that it will not be sufficient to watch the videos to successfully complete the course.
The classroom sessions are dedicated to going through solutions for exercises and to clarifying or elaborating on concepts discussed in a chapter. Solutions will be presented by the students, based on R Markdown documents they sent in. (See the section Examination for more detail)
Sessions
1) The Golem of Prague [Introduction]
2) Small Worlds and Larger Worlds [Bayesian data analysis]
3) Sampling the Imaginary [Obtaining and analyzing posterior distributions]
4) Geocentric Models [Linear regression]
5) The Many Variables & the Spurious Waffles [Multiple regression and an introduction to DAGs]
6) The Haunted DAG & Causal Terror [Causal analysis and choice of covariates]
7) Ulysses’ Compass [Model complexity and model comparison]
8) Conditional Mantees [Interaction of predictor variables]
(9) Markov Chain Monte Carlo])
10) Big Entropy and the Generalized Linear Model [Maximum entropy and choice of likelihood functions]
11) God Spiked the Integers [Multiple regression for count and categorical outcomes]
12) Monsters and Mixtures [Multiple regression for zero inflation and ordinal outcomes]
13) Models with Memory [Multilevel (hierarchical) regressions]
Examination
8 Credit points are given for continuous participation in the seminar. Continuous participation means solving and presenting exercises and participation in group discussions. All exercises shall be sent in as an R Markdown document. Submission of exercises from the chapters:
- 3 easy exercises for each chapter (distributed randomly to participants)
- 2 medium exercises for each chapter (distributed randomly to participants)
- 3 hard exercises across all chapters, which need to be presented in the seminar
- Exercises can be completed in teams of 2
- Exercises will be completed with either with the rethinking packages and base are or with the tidyverse & brms.
- Submission for each chapter:
- clarification or discussion question
- 3-5 lessons learned
Richard McElreath (2020) Statistical Rethinking: A Bayesian Course with Examples in R and Stan. 2nd Edition. Chapman and Hall/CRC (DOI: https://doi.org/10.1201/9780429029608)