robust fitting and density estimation

After my binary programming failures of yesterday, Bovy implemented a Gibbs sampler and solved my problem overnight. But then in discussing the issues, we concluded—as we always do—that the only principled way to deal with bad data or outliers is to model them. This means performing density estimation or modeling of the distribution function for the outliers simultaneously with performing the fit on the inliers, so all the data can be generatively modeled as a two-component mixture. One component is the inliers, with model parameters fitting those inliers. The other is the outliers, with model parameters describing the distribution of outliers. I think we may have to switch to that in the robust fitting section of the now-infamous fitting a straight line document.

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