# 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:

$p(\vartheta | d) = \frac{p(d | \vartheta) p(\vartheta)}{p(d)}$

## Subtypes¶

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.

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