5. Bayesian posteriors#
In this chapter we have a hands-on look at one- and two-dimensional probabilitiy distributions.
We start with a demonstration Jupyter notebook on 📥 Exploring PDFs using Python libraries, with follow-up questions in Follow-up questions and answers to the Exploring PDFs section..
We continue with Gaussians: A couple of frequentist connections, with insight on why Gaussian distributions are so common, including a first look at the central limit theorem, plus some contrasts to frequentist statistics, such as the difference between Bayesian credible intervals and frequentist confidence intervals. Also in this section is a demonstration notebook on the 📥 Visualization of the Central Limit Theorem
The posteriors we will encounter will in general be multi-dimensional. We consider some aspects beyond one-dimensional (1D) posteriors in Interpreting 2D posteriors.
In 📥 Demonstration: Sum of normal variables squared we identify the origin of the \(\chi^2\) distribution function from the sum of squares of Gaussian random variables.