How can you calibrate Bayesian models with ease?

1 Why calibrate?

Calibration is essential for any statistical model, but especially for Bayesian ones, because they involve subjective choices and uncertainty. By calibrating your model, you can assess how sensitive it is to the prior distribution, the likelihood function, and the data. You can also compare different models and select the one that best represents the data and the problem. Calibration can help you avoid overfitting, underfitting, bias, and inconsistency in your model.

3 What to use?

Calibrating Bayesian models requires algorithms and software that can handle the complexity and uncertainty of the Bayesian framework. Markov chain Monte Carlo (MCMC) is a family of algorithms that generate random samples from the posterior distribution, which can be used to estimate the parameters, uncertainty, and predictive performance. Variational inference (VI) is another family of algorithms that approximate the posterior distribution, while Automatic Differentiation Variational Inference (ADVI) uses automatic differentiation to compute gradients. To use these algorithms, you need software such as Stan, PyMC3, or JAGS. Stan is a probabilistic programming language with a flexible syntax and fast compiler, while PyMC3 is a Python library with a user-friendly syntax and rich set of distributions and models. JAGS has a similar syntax to BUGS, a classic software for Bayesian modeling, and can be called from multiple languages.

4 How to learn?

To learn how to calibrate Bayesian models with ease, you need to have a solid foundation of the Bayesian principles and methods, as well as the algorithms and software that can implement them. Fortunately, there are many resources available online, such as books, courses, tutorials, blogs, and podcasts. For example, Bayesian Data Analysis by Gelman et al. is a classic and comprehensive book that covers the theory and practice of Bayesian modeling with examples and exercises in R and Stan. Statistical Rethinking by McElreath is a modern and engaging book that introduces the concepts and applications of Bayesian modeling with examples and exercises in R and Stan. Bayesian Methods for Hackers by Davidson-Pilon is a practical and fun book that teaches the basics and tricks of Bayesian modeling with examples and code in Python and PyMC3. Doing Bayesian Data Analysis by Kruschke is a friendly and thorough book that guides you through the steps and details of Bayesian modeling with examples and code in R and JAGS. Introduction to Empirical Bayes by Robinson is a concise and clear book that shows you how to use empirical Bayes methods to improve your estimates and predictions with examples and code in R. Learn Bayes Nets by Hejazi is a free online course that teaches you how to build and analyze Bayesian networks with examples and code in R and Stan. Bayesian Analysis with Python by Martin is a hands-on book that teaches you how to use Python and PyMC3 to perform Bayesian analysis with examples and code in Python and PyMC3. Finally, Rethinking Statistics by Solomon Kurz is a free online course that teaches you how to use Stan and R to replicate and extend the examples from the Statistical Rethinking book, while Bayesian Statistics Made Simple by Allen Downey is another free online course offering an introduction to the basics of Bayesian statistics with examples in Python and PyMC3.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?