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.


  1. Hi David,

    I hadn't read the paper on fitting distributions before---very interesting. Sort of similar to some work I have done on the BH mass distribution from XRB observations. You might also be interested in this paper by my colleague, Ilya Mandel, that could have been titled "don't add the PDFs": http://arxiv.org/abs/arXiv:0912.5531

  2. "I think maybe I need to write a Data Analysis Recipes on this."

    Yes, Please!

  3. "Fundamentally, adding up pdfs is never a good idea."

    Nitpicky comment: Marginalization is a weighted sum of PDFs. ;-) Just being silly here, it's got nothing to do with what you're saying.

    I believe Loredo had a paper a few years back where he showed why hierarchical modelling is needed in that situation (it was the paper where I first heard about what you call "extreme deconvolution").

  4. Jeffrey Newman24 March, 2013 14:46

    You'll find this point made in the upcoming CANDELS photo-z methods paper as well. . . hierarchical techniques end up not being too expensive in that application (but are outperformed by taking the median of the ~5 best photo-z estimates).