5. 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 One- and two-dimensional PDFs and then a demonstration notebook exploring PDFs using Python libraries (📥 Demo: Exploring PDFs).

• We continue with More on Gaussian distributions, 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 (📥 Demo: Visualization of the Central Limit Theorem).

• Some frequentist connections 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.