--- title: Bayesian Statistics description: Bayesian statistics is a mathematical framework that applies probability to statistical problems, updating beliefs as new data is observed. You will understand how to construct prior distributions, compute posterior probabilities, and perform Bayesian inference. category: programming-tech subcategory: data-science difficulty: beginner, intermediate, advanced url: /subject/bayesian-statistics --- # Bayesian Statistics Bayesian statistics is a mathematical framework that applies probability to statistical problems, updating beliefs as new data is observed. You will understand how to construct prior distributions, compute posterior probabilities, and perform Bayesian inference. ## Available Resources 1 Videos • 4 Books • 2 Courses • 6 Websites ## Websites ### 1. PyMC Documentation Official documentation for PyMC, the Python library for probabilistic programming, with installation guides, API reference, and worked example notebooks. Covers specifying priors and likelihoods, running MCMC samplers, and checking posterior results. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.pymc.io/welcome.html **Tags:** pymc, probabilistic-programming, python, mcmc, bayesian-inference ### 2. Think Bayes 2e Allen Downey's free online textbook teaches Bayesian statistics computationally in Python, with every chapter as a runnable Jupyter notebook. Covers distributions, MCMC, regression, and survival analysis, using code and simulation instead of heavy calculus. **Difficulty:** Beginner | **Price:** Free **Link:** https://allendowney.github.io/ThinkBayes2/ **Tags:** bayesian-inference, python, jupyter, computational-statistics, free-textbook ### 3. Bayes Rules! Free online textbook by Johnson, Ott, and Dogucu covering Bayes' rule, conjugate families, MCMC simulation, and hierarchical regression models. Exercises use R with rstan and rstanarm, so readers finish able to fit and check Bayesian models. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.bayesrulesbook.com/ **Tags:** bayesian-inference, r, mcmc, regression, hierarchical-models, free-textbook ### 4. mc-stan.org Official site for Stan, a probabilistic programming language for Bayesian statistical modeling; it offers tutorials, documentation, case studies, and download/install guides, plus interfaces and examples for R, Python, and CmdStan. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mc-stan.org **Tags:** websites, technology-computer-science, statistics-data-science ### 5. seeing-theory.brown.edu Seeing Theory is an interactive, browser-based resource from Brown University that uses visual simulations to explain fundamental probability and statistics concepts. It offers interactive demos and explanations on topics like probability, distributions, sampling, the central limit theorem, confidence intervals, hypothesis testing, and Bayesian reasoning. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://seeing-theory.brown.edu **Tags:** websites, technology-computer-science, data-science--ai ### 6. stats.stackexchange.com Stats Stack Exchange is a Q&A community for statistics professionals and enthusiasts, featuring questions and expert answers on topics from probability and inference to data analysis and experimental design. It’s a practical resource for learning statistical concepts, getting help with methods, and discussing real-world data problems. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://stats.stackexchange.com **Tags:** websites, technology-computer-science, data-science--ai ## Videos ### 1. Introduction to Bayesian data analysis - part 1: What is Bayes? First part of Rasmus Bååth's video introduction to Bayesian data analysis, explaining the approach conceptually before the math. Viewers see how prior information, observed data, and a generative model combine to produce a posterior distribution. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=3OJEae7Qb_o **Tags:** bayesian-inference, statistics, lecture, introductory ## Courses ### 1. Statistical Rethinking Learn Bayesian statistics with Richard McElreath's popular Statistical Rethinking course. Master modeling & inference through engaging lectures! **Difficulty:** Intermediate | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLDcUM9US4XdPz-KxHM4XHt7uUVGWWVSus **Tags:** bayesian-inference, statistical-modeling, causal-inference, r, lectures ### 2. Bayesian Statistics: From Concept to Data Analysis This course introduces the Bayesian approach to statistics, starting with the concept of probability and moving to the analysis of data. We will learn about the philosophy of the Bayesian approach as well as how to implement it for common types of data. We will compare the Bayesian approach to the more commonly-taught Frequentist approach, and see some of the benefits of the Bayesian approach. In particular, the Bayesian approach allows for better accounting of uncertainty, results that have more intuitive and interpretable meaning, and more explicit statements of assumptions. This course combines lecture videos, computer demonstrations, readings, exercises, and discussion boards to create an active learning experience. For computing, you have the choice of using Microsoft Excel or the open-source, freely available statistical package R, with equivalent content for both options. The lectures provide some of the basic mathematical development as well as explanations of philosophy and interpretation. Completion of this course will give you an understanding of the concepts of the Bayesian approach, understanding the key differences between Bayesian and Frequentist approaches, and the ability to do basic data analyses. **Difficulty:** Beginner | **Language:** English | **Duration:** Four weeks of study, two-five hours/week depending on your familiarity with mathematical statistics. | **Price:** Free **Link:** https://www.coursera.org/learn/bayesian-statistics **Tags:** courses, mathematics-statistics, statistics-and-probability ## Books ### 1. Information Theory, Inference, and Learning Algorithms **Author:** David J. C. MacKay David MacKay's textbook, free to read online, covering entropy, data compression, noisy-channel coding, error-correcting codes, Bayesian inference, Monte Carlo methods and neural networks. Readers come to understand Shannon's coding theorems and apply probabilistic reasoning to communication and learning problems. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://www.inference.org.uk/mackay/itila/ **Tags:** information-theory, coding-theory, data-compression, bayesian-inference, machine-learning ### 2. Bayesian Data Analysis **Author:** Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin Graduate-level reference by Gelman, Carlin, Stern, and Rubin covering Bayesian modeling from single-parameter models to hierarchical models, model checking, and computation. Readers gain the theory needed to build, fit, and criticize applied Bayesian models. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0412039915?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, statistics-and-probability ### 3. Doing Bayesian Data Analysis **Author:** John K. Kruschke Kruschke teaches Bayesian inference step by step with worked R and JAGS code, moving from probability basics to hierarchical models and Bayesian analogues of t-tests, ANOVA, and regression. Assumes only introductory statistics. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0123814855?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, statistics-and-probability ### 4. Introduction to Bayesian Statistics **Author:** William M. Bolstad Undergraduate textbook that introduces Bayesian inference alongside the frequentist methods students already know, covering discrete and continuous priors, conjugate analysis, and Bayesian inference for means, proportions, and simple regression. Readers finish able to carry out basic Bayesian analyses by hand. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0470141158?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, statistics-and-probability --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/bayesian-statistics