Applied Bayesian Data Analysis With R

Build powerful statistical models, simulate uncertainty, & master Bayesian thinking using real data & modern tools in R

What you'll learn

High level understanding of fundamental concepts in Bayesian data analysis

Hamiltonian and NUTS sampling

brms, Stan, and tools around these packages

Bayesian approaches

Understand where to go for more information and use that information for Bayesian data analysis methods in your own work

Foundations of Bayesian thinking: Understand how to frame uncertainty, update beliefs with evidence, and interpret results using posterior probabilities.

Bayesian inference using MCMC: Get hands-on with Markov Chain Monte Carlo, Metropolis-Hastings, and Hamiltonian Monte Carlo (HMC), with clear explanations of h

Model fitting with brms: Learn to run Bayesian regression models using familiar R syntax, inspect MCMC chains, and evaluate model fit with posterior predictive

Custom modeling with Stan: Write your own Bayesian models in Stan to handle more complex or non-linear problems.

Model diagnostics and workflow: Master tools to detect convergence issues, perform cross-validation, and make informed modeling decisions through a robust Bayes

Requirements

Familiarity with linear regression and generalized linear models and ideally mixed effects models

Experience with R and access to R and R Studio

May or may not have had exposure to Bayesian methods in JAGS, BUGS, etc.

Description

This comprehensive course will take you on a journey into the world of Bayesian statistics, one of the most powerful and intuitive frameworks for reasoning under uncertainty. Using real data and hands-on coding in R, you'll learn how to build, evaluate, and interpret Bayesian models using cutting-edge tools like brms and Stan.Whether you're a data scientist aiming to deepen your statistical toolkit, a social scientist wanting to model complex effects, or a beginner curious about Bayesian reasoning, this course is designed to bring clarity, confidence, and capability to your analysis.We begin by reshaping how you think about probability. Rather than treating it as a long-run frequency, you’ll learn to think of probability as a degree of belief—a perspective that naturally leads to Bayesian reasoning. Through intuitive explanations and code-based demonstrations, we’ll explore how prior beliefs can be updated using new data to form posterior conclusions.From there, we move into core computational methods that allow modern Bayesian analysis to scale. You’ll master Markov Chain Monte Carlo (MCMC) sampling—starting with the Metropolis-Hastings algorithm and moving toward Hamiltonian Monte Carlo (HMC) and NUTS, the algorithms that power modern Bayesian engines like Stan.But theory alone isn’t enough.That’s why this course is packed with practical, real-world applications using the powerful and user-friendly brms package in R—a front-end to Stan that lets you fit sophisticated models using familiar R syntax. You'll build Bayesian linear regressions, simulate data, check assumptions, and interpret your results like a pro.For those ready to go deeper, we’ll open the hood and dive into writing models directly in Stan, giving you complete control over model structure, likelihoods, and priors. You’ll explore everything from simple linear models to non-linear growth curves and hierarchical structures.We’ll also equip you with the tools needed for model validation and selection, including posterior predictive checks, cross-validation, and Expected Log Predictive Density (ELPD). You’ll learn how to diagnose convergence issues, identify divergent transitions, and follow a principled Bayesian workflow from model formulation to decision-making.By the End of This Course, You Will:Be able to think like a Bayesian, incorporating prior knowledge and updating beliefs using dataConfidently use MCMC methods to fit and diagnose Bayesian modelsPerform Bayesian regression analysis using brms, and know when and how to customize models using StanUnderstand how to simulate from priors and posteriors, check model fit, and communicate uncertainty clearlyApply a principled Bayesian workflow to real-world data problems, from data exploration to final model validation

Overview

Section 1: Foundations of Bayesian Thinking & MCMC

Lecture 1 Introduction - Thinking Like a Bayesian

Lecture 2 Downloading the excersize files

Lecture 3 Bayesian updating with a grid search approach

Lecture 4 What makes Bayesian methods different in a practical sense

Lecture 5 Why go Bayesian

Lecture 6 Course Objectives

Lecture 7 Markov Chain Monte Carlo (MCMC)

Lecture 8 Hamiltonian and NUTS MCMC

Lecture 9 MCMC Chain Diagnostics

Lecture 10 MCMC Chain Diagnostics Exercise

Lecture 11 Introduction to Priors

Section 2: Bayesian Regression Modeling in R with brms

Lecture 12 Posterior and prior predictive simulation

Lecture 13 Posterior predictive simulation exercise

Lecture 14 An introduction to applied Bayesian regression using brms

Lecture 15 brms intro continued: inspecting the MCMC chains

Lecture 16 brms intro continued: posterior predictive checking

Lecture 17 brms intro continued: interpreting the coefficients

Lecture 18 brms intro continued: summarizing parmeter posteriors

Lecture 19 Priors in brms including the treatment of the intercept

Section 3: Custom Modeling - Writing and Fitting Bayesian Models with Stan

Lecture 20 Introduction to Stan syntax

Lecture 21 Stan linear regression example

Lecture 22 Non-linear growth model in Stan

Lecture 23 Cross validation + ELPD

Section 4: Advanced Diagnostics and the Bayesian Modeling Workflow

Lecture 24 Divergent transitions

Lecture 25 Bayesian workflow slides

Lecture 26 Bayesian workflow example

Lecture 27 Closing remarks

Students of statistics, data science, and machine learning,Researchers seeking a strong theoretical foundation in Bayesian methods,Analysts and decision-makers interested in probabilistic reasoning and forecasting,Anyone with a basic understanding of probability and statistics who wants to learn Bayesian statistics step by step,R users interested in probabilistic modeling and uncertainty quantification.,Practitioners who need to build and evaluate custom models.,Data analysts, statisticians, and researchers transitioning from frequentist to Bayesian methods.