Bayesian Inference

In a Bayesian Inference problem, we have a probability model that consists of a conditional probability \(p(d | \vartheta)\) of data \(d\) given a set of variables \(\vartheta\), and a prior \(p(\vartheta)\) for the problem variables.

The solver is applied to the posterior distribution of the problem variables:

\[p(\vartheta | d) = \frac{p(d | \vartheta) p(\vartheta)}{p(d)}\]


For data stemming from a computational model, for which you only want to choose a noise distribution and variable prior, a Bayesian Reference Likelihood problem can be used.

A Custom Likelihood problem allows any kind of user defined probability model \(p(d | \vartheta)\).

If your problem has additional (latent) variables in addition to the parameters of interest, the subtypes of Bayesian Latent Variable problems can be used.