Consider the clutter problem of Tom Minka where the goal is to get posterior of the mean of one Gaussian component. The likelihood is a mixture of two Gaussians, one of which is just noise. The other component is the true data generator. Say I use EP to approximate
this likelihood term with one Gaussian by moment matching.

- What happens to the inferred mean if I perturb the mean/variance of this approximate Gaussian ?
- Which one affects the inferred mean more between having an inaccurate mean (in approximate factors) or an inaccurate variance ?
- In general, is there some work that analyzes how EP behaves as we vary approximate factors ?