List of resources for bayesian inference

• Statistical Rethinking
• Bayesian Data Analysis
• Probability Theory: The Logic of Science
• The Bayesian Choice
• Bayesian methods for hackers
• Bayesian Analysis with Python | errata and extra material

• BUGS: Bayesian Inference Using Gibbs Sampling. Oldest of the Bayesian inference platforms, tried and tested. Has a Windows friendly version, WinBUGS. R, python and many other language bindings, GUIs and
• JAGS: Just another Gibbs sampler, similar to BUGS - focused on cross-platform, usability. Also tried and tested. R and python bindings too.
• Stan: Full-featured Bayesian inference with R and python bindings. Based on Hamiltonian MC and NUTS. Current favorite of the community it seems with lots of examples, docs.
• PyMC3: Probabilistic programming in Python/Theano. PyMC4 is in dev, will use Tensorflow as backend. Great API and interface, but hindered by Theano's deprecation. PYMC4 promises great things.
• edward2/tfprobability: Probabilistic programming in tensorflow. Scalable models, but little docs.
• Zhusuan: Another probabilistic programming framework built on tensorflow.
• Pyro: Probabilistic programming in Pytorch. Good docs, scalable models too.
• Brancher: Probabilistic inference based on auto diff and variational models, also based on Pytorch.
• LaplacesDemon: Mysterious probabilistic programming package in R with a cult following.
• WebPPL: Probabilistic programming in the browser.
• Turing.jl: Probabilistic programming in Julia, by Zoubin Ghahramani's lab.
• Infer.NET: Specializes in running probabilistic inference in factor graphs (Expectation Propagation, Variational Inference). Programs written in .NET.

• brms : Generalized linear/non-linear multilevel models, uses Stan.
• R-INLA : Latent Gaussian models via Integrated Nested Latent Approximations. Really fast compared to MCMC.
• bayesmix: Finite mixture models with JAGS in R
• lmm: Linear mixed models fitted with MCMC

• List of Bayesian inference packages for R: Comprehensive list for all Bayesian inference in R
• ArviZ: ArviZ is a Python package for exploratory analysis of Bayesian models. Includes functions for posterior analysis, sample diagnostics, model checking, and comparison. Works with PyMC3, PyStan, emcee, Pyro and TensorFlow Probability.
• StatSim: Browser-based interface to create, share, and perform inference on probabilistic models. Powered by WebPPL and PyMC3.

• Michael Clark's Blog on Stat modeling, Bayesian inference
• Bayesian Spectacles

• Count Bayesie: Will Kurt from "Get Programming with Haskell" fame explains basic probability and stats concepts through a Bayesian lens in a fun way.
• How to become a Bayesian in eight easy steps
• Introduction to Bayesian Statistics: Course lectures by Brendon Brewer (University of Auckland)
• Michael Jordan's Bayesian Statistics Course Notes

• The MCMC interactive gallery: Build intuition for common MCMC routines using interactive demos. A walkthrough of the demos can be found here.
• The MCMC handbook intro to MCMC: A no-frills intro to MCMC
• Scaling up Bayesian inference: For Big Data™

• Intro to variational inference via mean field approx
• David Blei's Variational Inference tutorial
• Expectation Maximization and Variational Inference

• Understanding Empirical Bayes
• Efron's overview of Empirical Bayes

• Collection of tutorials on non-parametrics
• Infinite mixture models
• A Visual Exploration of Gaussian Processes

• A gentle INLA tutorial
• Step by step INLA tutorial

• Yarin Gal's talk on Bayesian Deep Learning: Blog post of the talk is also very informative, check it out here
• What is a variational autoencoder?

• Probabilistic Numerics: View all numeric optimization through a Bayesian lens

Indexed here, these deserve a list all to themselves:

• Principled Bayesian Worflow: What to know and what to look for when doing Bayesian inference.
• Conceptual introduction to Hamiltonian MC
• Identifying Bayesian Mixture Models
• Diagnosing Biased Inference Using Divergences

• Michael Jordan
• Zoubin Ghahramani
• Danielle Navarro
• Michael Betancourt
• Dan Simpson
• Thomas Wiecki
• David Blei
• Andrew Gelman
• Dustin Tran
• Yarin Gal