Notes for an advanced course on Bayesian statistics

Project Name | Stars | Downloads | Repos Using This | Packages Using This | Most Recent Commit | Total Releases | Latest Release | Open Issues | License | Language |
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Probabilistic Programming And Bayesian Methods For Hackers | 25,288 | a month ago | 196 | mit | Jupyter Notebook | |||||

aka "Bayesian Methods for Hackers": An introduction to Bayesian methods + probabilistic programming with a computation/understanding-first, mathematics-second point of view. All in pure Python ;) | ||||||||||

Pgmpy | 2,295 | 6 | 5 | 7 days ago | 18 | June 30, 2022 | 238 | mit | Python | |

Python Library for learning (Structure and Parameter), inference (Probabilistic and Causal), and simulations in Bayesian Networks. | ||||||||||

Bayesian Modelling In Python | 2,202 | 6 years ago | Jupyter Notebook | |||||||

A python tutorial on bayesian modeling techniques (PyMC3) | ||||||||||

Imodels | 1,068 | 2 | a day ago | 26 | July 03, 2022 | 23 | mit | Jupyter Notebook | ||

Interpretable ML package 🔍 for concise, transparent, and accurate predictive modeling (sklearn-compatible). | ||||||||||

Easystats | 880 | 2 days ago | 43 | gpl-3.0 | R | |||||

:milky_way: The R easystats-project | ||||||||||

Statistical Rethinking With Python And Pymc3 | 674 | 5 years ago | 2 | Jupyter Notebook | ||||||

Python/PyMC3 port of the examples in " Statistical Rethinking A Bayesian Course with Examples in R and Stan" by Richard McElreath | ||||||||||

Jasp Desktop | 610 | 4 days ago | 23 | agpl-3.0 | C++ | |||||

JASP aims to be a complete statistical package for both Bayesian and Frequentist statistical methods, that is easy to use and familiar to users of SPSS | ||||||||||

Pydlm | 400 | 1 | 1 | 2 years ago | 13 | December 19, 2018 | 29 | bsd-3-clause | Python | |

A python library for Bayesian time series modeling | ||||||||||

Elfi | 247 | 14 days ago | 6 | June 13, 2022 | 10 | bsd-3-clause | Python | |||

ELFI - Engine for Likelihood-Free Inference | ||||||||||

Bat.jl | 163 | 15 days ago | 17 | other | Julia | |||||

A Bayesian Analysis Toolkit in Julia |

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Readme

Data don't speak for themselves

Bayesian statistics is rising in popularity in the astrophysical literature. It is no longer a debate: "work in Bayesian statistics now focuses on applications, computations, and models. Philosophical debates [...] are fading to the background" (Bayesian Data Analysis, Gelman et al.). This is happening for two main reasons: faster computers and more complex models. In order to keep up, it is important to understand the fundamentals of Bayesian statistics, but it is as important to know how to deal with data analysis applications.

In this course I want to provide a brief introduction to advanced concepts in Bayesian statistics. Emphasis will be on "intuition" and "computation". No coin tossing, only real applications that relate to our day-to-day problems.

The idea is to present some statistical results in an intuitive manner and then turn to computational methods. By the end of the course, the students should be able to understand:

THEORY

- what are the main differences between frequentist and Bayesian statistics . problems with p-values, confidence intervals and null hypothesis testing
- the basic rules of probability theory
- how to assign probability distributions . the role of priors . the likelihood
- the simplest models in Bayesian statistics: . linear regression, . beta-binomial model, . hierarchical models

PRACTICE

- what is an MCMC, how it works and why it works; shortcomings (and alternatives)
- code an MCMC from scratch to sample a distribution
- for the (weighted) linear regression model . build the probabilistic graphical model and derive the posterior distribution . use our MCMC to sample the posterior for slope and intercept . solve the problem with a "black box" MCMC sampler in Python
- calculate the evidence integral to do model comparison

This work is licensed under a Attribution-ShareAlike 4.0 International license.

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