# Observation Models¶

All observation models define a likelihood for producing data $$x_n$$ from some cluster-specific density with parameter $$\phi_k$$:

$p(x | \phi, z) = \prod_{n=1}^N p( x_n | \phi_k )^{\delta_k(z_{n})}$

Supported Bayesian methods require specifying a (conjugate) prior:

$p(\phi) = \prod_{k=1}^K p(\phi_k)$

## Variational methods for observation models¶

The links below describe the mathematical and computational details for performing standard variational optimization for supported observation models: