I have a set of observations that can be thought of as random samples from a 2D gaussian (with some noise added). The samples are determined by a best-fit model which has an associated evidence value.
I can fit a 2D gaussian to one of these observations and from its covariance matrix $\bf \Sigma$ determine useful quantities such as axis ratio and orientation.
I can also combine these sets of random samples to get much better coverage in space and improve my fit statistics and overall ability to recover axis ratio and orientation etc.
My question is:
How can I combine these random samples such that they are weighted by the evidence associated with the model they represent?
Can it be done by fitting a gaussian to each sub-set of samples and then combining their covariance matrices, weighted by their evidence?