(sec:MoreOnPDFs)=
# More on PDFs

In this chapter we collect material addressing various aspects of  probability distributions (PDFs).
The sections are not required to be studied sequentially.
In some cases there will be references to exercises or demonstration notebooks that appear later in the book.

* The posteriors we will encounter will in general be multi-dimensional. We first consider some aspects beyond one-dimensional (1D) posteriors in {ref}`sec:1and2dPDFs` and then a demonstration  notebook exploring PDFs using Python libraries ({ref}`demo:exploring-pdfs`).

* We continue with {ref}`sec:Gaussians`, which has insight on why Gaussian distributions are so common, including a first look at the central limit theorem (CLT).
Next is a demonstration notebook on the CLT ({ref}`demo:visualization-of-the-central-limit-theorem`).

* {ref}`sec:SomeFrequentistConnections` provides some contrasts to Bayesian statistics, such as the difference between Bayesian credible intervals and frequentist confidence intervals and the origin of the $\chi^2$ distribution function from the sum of squares of Gaussian random variables.