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Bayesian Data Analysis

HardData ScienceStatistics20 chapters

Build, fit, and evaluate Bayesian models using modern computation — MCMC and approximations — for inference in linear, hierarchical, and nonparametric regression.

What This Course Covers

Bayesian Data Analysis is structured into 20 chapters that build on each other progressively:

Chapter 1: Foundations of Bayesian Inference▼
Chapter 2: Single-Parameter Models▼
Chapter 3: Multiparameter Models▼
Chapter 4: Asymptotics and Connections to Non-Bayesian Approaches▼
Chapter 5: Hierarchical Models▼
Chapter 6: Model Checking▼
Chapter 7: Evaluating and Comparing Models▼
Chapter 8: Modeling Data Collection▼
Chapter 9: Decision Analysis▼
Chapter 10: Introduction to Bayesian Computation▼
Chapter 11: Markov Chain Monte Carlo Basics▼
Chapter 12: Advanced Markov Chain Monte Carlo▼
Chapter 13: Approximate Inference Methods▼
Chapter 14: Linear Regression▼
Chapter 15: Hierarchical Linear Models▼
Chapter 16: Generalized Linear Models▼
Chapter 17: Robust Inference and Missing Data▼
Chapter 18: Flexible Regression with Basis Functions and Gaussian Processes▼
Chapter 19: Finite and Infinite Mixture Models▼
Chapter 20: Dirichlet Process Models▼

Each chapter combines interactive AI tutoring with hands-on examples. After you learn the material, Lambdio's spaced repetition algorithm schedules review sessions at optimal intervals — so you retain concepts and techniques long-term.

How to Study Bayesian Data Analysis on Lambdio

Lambdio's AI-powered platform adapts to how Data Science courses are best learned. Here's our recommended approach:

Learning Mode
Standard Mode — for first-time learning of each chapter
Review Modes
Standard, Quiz — for spaced repetition reviews
Learning Priority
High Priority — controls how often the algorithm schedules reviews

Bayesian Data Analysis is a dense, mathematically rigorous course that stacks one framework on another — from Bayes' rule and conjugacy to hierarchical models, MCMC, regression, and nonparametric methods — so Standard Mode is the right way to learn it. Standard Mode delivers structured exposition of model specifications, posterior derivations, and computational algorithms with built-in comprehension checks, which suits this procedural, formula-driven material far better than Socratic questioning. Socratic Mode is a poor fit for a course centered on posterior derivations, Markov chain Monte Carlo algorithms, and generalized linear model specifications. Because the course is rated Hard and each chapter assumes fluency with the last, High priority is the ideal setting: a frequent spaced-repetition schedule keeps foundational results such as conjugacy, full conditional distributions, and convergence diagnostics sharp, since chapters 11 through 20 lean on them constantly. During review, pair Standard Mode with Quiz Mode to rapidly verify recall of model forms, algorithm steps, and the assumptions behind each method before an exam or a research project.

Interactive Quiz

Test your knowledge with these sample questions from the course. Tap an answer to see if you're right:

Q1: Which sequence of steps describes the idealized Bayesian data analysis workflow?
Q2: Which distribution serves as the conjugate prior for a binomial likelihood?
Q3: How is the marginal posterior distribution of a parameter of interest obtained in a multi-parameter model?
Q4: In a hierarchical model, what role do hyperparameters play?
Q5: What is the purpose of posterior predictive checking?
Q6: Which model comparison criterion is fully Bayesian because it averages over the posterior rather than conditioning on a point estimate?
Q7: Under what conditions is a missing-data mechanism ignorable?
Q8: What does the stick-breaking construction represent in a Dirichlet process model?
Q9: Why is Hamiltonian Monte Carlo often more efficient than random-walk Metropolis for high-dimensional posteriors?

What You'll Be Able to Do After This Course

  • ✓Explain Bayesian inference as belief updating and derive posterior distributions using Bayes' rule
  • ✓Build single-parameter and multi-parameter models with conjugate, noninformative, and weakly informative priors
  • ✓Construct and interpret hierarchical models, hyperpriors, and shrinkage estimates for grouped data
  • ✓Perform posterior predictive checking, sensitivity analysis, and model comparison with information criteria and cross-validation
  • ✓Model data-collection mechanisms, ignorable missingness, and causal effects in surveys and experiments
  • ✓Implement Bayesian computation with Monte Carlo, Gibbs, Metropolis-Hastings, and Hamiltonian Monte Carlo methods
  • ✓Diagnose MCMC convergence and summarize posteriors using multiple chains, R-hat, and effective sample size
  • ✓Fit Bayesian linear, hierarchical, and generalized linear models, including robust and missing-data extensions
  • ✓Apply basis function, Gaussian process, finite mixture, and Dirichlet process models to flexible and nonparametric regression

Frequently Asked Questions

What mathematical background do I need for this course?▼
Do I need to know a programming language to take this course?▼
How long does it take to complete this course?▼
How is this course different from Bayesian Statistical Methods?▼
What is the difference between Bayesian and frequentist statistics?▼

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