Statistical ModelsΒΆ

Probability distributions are the building blocks of statistical models. Therefore we start showing how to construct user-defined distributions for a set of classical statistical inference problems.

In the following we will work with the random variable \({\bf X} \sim \nu_\pi\) defined over the probability space \((\Omega,\mathcal{F},P)\). The distribution \(\nu_\pi\) is assumed to be absolutely continuous with respect to the Lebesgue measure (\(\nu_\pi \ll \lambda\)), and thus adimts the density \(\pi\) such that

\[\nu_\pi(A) = \int_A \pi({\bf x}) d{\bf x} \;,\]

for all \(\nu_\pi\)-measurable sets \(A\).