do clusters dissolve? and don't add pdfs

Conversations continued with Fouesneau and Weisz; today they were about the evolution of stellar clusters. Fouesneau is working on using observations of clusters of different masses and ages to constrain models of cluster evolution and dissolution. It looks like at early ages (less than 0.1 Gyr), the cluster population is consistent with cluster conservation, but at old ages (greater than 1 Gyr), there must be cluster destruction or dissolution. We wrote down a probabilistic model for this process and a plan for how it could be inferred at the photometric-catalog level (rather than the inferred masses and ages level). Going to the photometric-catalog level permits inclusion of non-approximate completeness functions.

At one point in the conversation I fired up my don't co-add your posterior pdfs rant. If you have a bunch of posterior pdfs, one per object (one per cluster, in this case, in the mass–age parameter space), what is your best estimate for the true distribution in the parameter space? It is not the coaddition of the posterior pdfs. Perhaps it is counterintuitive, but it is better to histogram best-fit values than it is to co-add pdfs. The Right Thing To Do (tm) is to perform a hierarchical analysis (as in this paper), but that's expensive and non-trivial. Fundamentally, adding up pdfs is never a good idea. I think maybe I need to write a Data Analysis Recipes on this.