I did my homework for Marshall, writing up six dense pages on my thoughts about probabilistic inference of shear from galaxy observations. It focuses on importance-sampling approaches to weak lensing, a la my eccentricity paper. This new weak-lensing rant is the Nth document like this I have written; I have a whole github repository for unusable documents about weak gravitational lensing. The key thing I figured out is that you don't just need a prior over galaxy shapes (as I blogged the other day), you need a prior over all galaxy properties. Part of the reason is that the likelihood includes covariances between the shape and other properties. Part of the reason is that our prior also includes such covariances, at least if it is going to represent our actual prior knowledge. We are a long way from having a method, of course (did I use the word "unusable" above?) but if we can show that you can do this with a small number of samples per galaxy, it just might work.
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