Bayesian Statistics: From Concept to Data Analysis
Coursera
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.
More resources on Bayesian Statistics
Information Theory, Inference, and Learning Algorithms
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.
Doing Bayesian Data Analysis
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.
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.
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.
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.
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.