Bayesian data analysis is increasingly becoming the tool of choice for many data-analysis problems. This free course on Bayesian data analysis will teach you basic ideas about random variables and probability distributions, Bayes' rule, and its application in simple data analysis problems. You will learn to use the R package brms (which is a front-end for the probabilistic programming language Stan). The focus will be on regression modeling, culminating in a brief introduction to hierarchical models (otherwise known as mixed or multilevel models). This course is appropriate for anyone familiar with the programming language R and for anyone who has done some frequentist data analysis (e.g., linear modeling and/or linear mixed modeling) in the past.
Introduction: Why are Bayesian methods important for data analysts?
Here are some of the advantages of Bayesian methods over the standard frequentist approach used in data analysis:
- Prior knowledge/expertise can be incorporated into the data analysis
- Models can be flexibly specified to reflect the assumed generative process
- The results of the analysis – the posterior distributions of the parameters of interest – have an intuitive interpretation
- Hypothesis testing can be carried out in a more meaningful manner than the standard used null hypothesis significance testing
Prerequisites: Who is this course for?
We assume the following in this course:
- Basic familiarity with the programming language R, openHPI offers a free R course for Beginners (in German)
- Experience with data analysis using linear models
- It is helpful (but not necessary) to have had some exposure to linear mixed models using the R library lme4
- High-school mathematics (pre-calculus)
- Some basic concepts from probability theory (sum and product rule, conditional probability)
This course is not appropriate for participants who don't know R programming and who have no experience at all with data analysis.
Course outcomes: What will you learn from this course?
- Some basic ideas relating to random variables
- Some fundamental properties of probability distributions
- Application of Bayes' rule in data analysis
- The concept of likelihood and its role in Bayesian statistical modeling
- Bayesian regression models using brms (a front-end for Stan)
- How to visualize and interpret prior and posterior distributions
- How to generate prior and posterior predictive distributions for evaluating models
- How to interpret the results of simple regression models
After completing this course, you will be in a good position to learn how to use more advanced Bayesian methods, such as hierarchical models, finite mixture models, multinomial processing tree models, measurement error models, etc.
What you'll learn
- Bayesian statistics
- Data analysis
- Bayesian regression models using brms
Course contents
Week 0 - Initial Setup:
Installing R and RStudio, rstan, brms, and other necessary packages in R; Setting up R markdown for reproducible data analyses.
Week 1 - Introduction:
Learn the foundational ideas about random variables and probability distributions; Reading: Chapter 1 of the textbook (excluding the section on bivariate distributions).
Week 2 - Bayesian data analysis:
Understand Bayes' rule, derive the posterior using Bayes' rule; visualize the prior, likelihood, and posterior; distinguish the relationship between the prior, likelihood, and posterior; incorporate prior knowledge into the analysis; Reading: Chapter 2.
Week 3 - Computational Bayesian data analysis:
Derive the posterior through sampling; perform simple regression modeling of a simple button-pressing task using Stan/brms; do prior predictive distributions, sensitivity analysis, and different classes of prior; do posterior predictive distributions; derive the log-normal likelihood; Reading: Chapter 3.
Week 4 - Bayesian regression and hierarchical models:
Perform simple linear regressions using the normal and binomial likelihoods to answer the following research questions: (i) Does attentional load affect pupil size? (ii) Does trial id affect response times? (iii) Does set size affect recall accuracy? Take a brief look-ahead at linear mixed models; Reading: Chapter 4 and up to section 5.3 of chapter 5.
Final Exam:
Final Exam
