Course information
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.
Course
structure: How do you plan this course?
This four-week
course consists of
- A series of weekly video lectures
- Self-tests, weekly homework, and
programming tasks
- Supplementary reading materials
We expect a
weekly time commitment of 5-10 hours to complete the course, depending on your
prior knowledge.
Recommended
reading: Textbook
The course
follows the structure of an online textbook, which will be published by CRC
Press soon. You can view the textbook here.
What you'll learn
- Bayesian statistics
- Data analysis
- Bayesian regression models using brms
Who this course is for
- Students
- Researchers
- Data Analysts
- Scientists
- Anyone who wishes to do data analysis
Course contents
- 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.
- Week 1 - Introduction: Learn the foundational ideas about random variables and probability distributions. Reading: Chapter 1 of the textbook.
- 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.
- 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.
- 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.
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