Replace the isotropic variance 
with a covariance matrix 
:
![\begin{displaymath}\mbox{Pr}\left[ {\bf x}, \rho \vert {\bf C}, {\bf c} \right] ... ...i - {\bf c}_j)^T {\bf C}^{-1} ({\bf x}_i - {\bf c}_j) \right)} \end{displaymath}](img19.gif)
The likelihood model is specified entirely by the covariance C(t;t')between the expression levels at any two timepoints.
This is an example of a Gaussian process. By choosing C(t;t') appropriately we can model splines, Brownian motion, power spectra, rough periodicity and more.
In other words, Bayesian modeling allows one to rely on priors. This is often helpful when data are sparse.