element covariances, expectation-maximization

I had a phone conversation with Foreman-Mackey, in which we discussed measurement and inference. The question at hand is whether to hand-tune the coefficients of The Cannon to not permit it to use lines from element A in assessing the abundance of element B. Left to its own devices, the code will do such things, if element A and element B are covariant in the training set of stars! If you permit the code to use A lines to get B abundances, you will probably get more precise answers (because there really is information there) but it will be harder for a user of the code output to use the output responsibly (if, say, he or she is fitting models of abundance patterns). This is yet another example of the (obvious) point that your data analysis decisions depend on your (or your user's) utility.

In other news, in reading about microscopy data-analysis methods, I finally understood the point of the E-M algorithm: It optimizes a marginalized likelihood, without requiring the user to explicitly compute the marginalized likelihood itself or its derivatives. It is funny that it took me so long to understand this, when I have about four or five papers in which we developed, proved, and used E-M algorithms!

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