Today I was finally back up at MPIA. I spent a good fraction of the day talking with Doug Finkbeiner (Harvard), Josh Speagle (Harvard) and others about probabilistic catalogs. Both Finkbeiner's group and my own have produced probabilistic catalogs. But these are not usually a good idea! The problem is that they communicate (generally) posterior information and not likelihood information. It is related to the point that you can't sample a likelihood! The big idea is that knowledge is transmitted by likelihood, not posterior. A posterior contains your beliefs and your likelihood. If I want to update my beliefs using your catalog, I need your likelihood, and I don't want to take on your prior (your beliefs) too.
This sounds very ethereal, but it isn't: The math just doesn't work out if you get a posterior catalog and want to do science with it. You might think you can save yourself by dividing out the prior but (a) that isn't always easy to do, and (b) it puts amazingly strong constraints on the density of your samplings; unachievable in most real scientific contexts. These problems are potentially huge problems for LSST and future Gaia data releases. Right now (in DR2, anyway) Gaia is doing exactly the correct thing, in my opinion.
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