model-free or badly modeled?

Robyn Sanderson (Groningen) is in town to finish our paper (with Helmi) on inferring gravitational potentials using information theory. Our method looks for generic clustering in action-space; it is "model-free" in the sense that it doesn't specify a model; it doesn't even assume the stars are on streams (and it doesn't need to know how many streams, or which stars are in which streams, or whether the streams are really shells, etc). The flip side of this is that it must, therefore, be (implicitly) a bad model.

One way of looking at it is that our method provides an estimator (a point estimate) of the potential. That estimator is either efficient or not. If it is efficient, it is the maximum-likelihood estimator for some model that we have never specified and therefore don't know. That can't be good! Indeed we can see that the estimator is biased, and the bias is bigger than the variance.

However, all that said, the point of this project is to explore the possibility that phase-space is structured, and be agnostic about that structure. This is complementary to my usual kinds of approaches, that make explicit assumptions about the causal or generative process of any structure we are using for inference. The method is (fairly) fast and seems to work, so we are writing.

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