Introduction to Bayesian Data Analysis

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Week 0 - Initial Setup

Please install the latest versions of R and RStudio, rstan, brms, and other necessary packages in R. In order to get the most out of this course, please read the textbook chapters 1-4 (the textbook link is provided below) as the course progresses. Each chapter belongs to the corresponding week in this course.

Welcome to the Course

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Preparatory R course (optional)

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Textbook to accompany the course (available online)

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General course information: Introduction to Bayesian Data Analysis

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Week 1 - Introduction

Learn the foundational ideas about random variables and probability distributions. Reading: Chapter 1 of the textbook.

Welcome to Week 1

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Pre-Course Survey

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1.1 Discrete random variables

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1.2 Discrete random variables (The binomial)

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Binomial distribution quiz

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1.3 Continuous random variables

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1.4 Continuous random variables (example: the normal distribution)

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1.5 Continuous random variables (example: the normal distribution)

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Normal distribution quiz

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1.6 Maximum likelihood estimates

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1.7 Bivariate and multivariate distributions (Discrete case)

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Bivariate distribution quiz

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1.8 Bivariate and multivariate distributions (Continuous case)

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Practical self-test for Week 1

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Homework - Week 1

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Week 2 - Bayesian data analysis

Understand Bayes' rule, derive the posterior using Bayes' rule; visualize the prior, likelihood, and posterior; distinguish between the prior, likelihood, and posterior; incorporate prior knowledge into the analysis. Reading: Chapter 2.

Welcome to week 2

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2.1 Bayes' Rule

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2.2 Bayes' rule in action (Binomial-Beta conjugate case)

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2.3 Bayes' rule in action (Poisson-Gamma conjugate case)

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2.4 Bayes' rule in action (Poisson-Gamma conjugate case - contd.)

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2.5 The Posterior Mean

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Selftest Week 2

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Homework - Week 2

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Week 3 - Computational Bayesian data analysis

Derive the posterior through sampling; build a simple linear regression model using brms; visualize prior predictive distributions, perform sensitivity analysis and posterior predictive checks. Reading: Chapter 3.

Welcome to Week 3

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3.1 Computational Bayes

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3.2 Computational Bayes

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3.3 Computational Bayes

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3.4 Computational Bayes

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3.5 Computational Bayes

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3.6 Computational Bayes

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3.7 Computational Bayes

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3.8 Computational Bayes

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Selftest Week 3

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Homework Week 3

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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.

Welcome to Week 4

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4.1 Regression models

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4.2 Regression models

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4.3 Regression models

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4.4 Regression models

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4.5 Regression models

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4.6 Regression models

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4.7 Regression models

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4.8 Regression models (hierarchical regression)

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Selftest Week 4

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Homework Week 4

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Please provide your feedback on the course.

I like, I wish - what is that?

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Post-Course Survey

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