coding and seminar

Lang and I got up early and pair-coded the arbitrarily covariant and heterogeneous errors in both dimensions case of fitting a line, with outlier rejection. I then showed this figure in the afternoon in the MPIA Hauskolloqium. My points of greatest emphasis were:

  • If you want to say you have the best fit model, then your model parameters better optimize a justified, scalar objective function. I mean justified as in non-arbitrary and scalar both in the sense of single-valued and in the sense of respecting relevant symmetries.
  • When you can create a generative model for your data, inference proceeds by maximizing the likelihood (or, better, sampling the posterior probability distribution function). You have no freedom about this; fitting does not involve much choice, at least at the conceptual level.
  • Markov-Chain Monte Carlo methods—in particular with the Metropolis algorithm—are very easy to implement and run, and they optimize even non-linear problems, explore multiple local minima, and automatically provide marginalizations over nuisance parameters.
The crowd was large and had great questions. Talks about technical issues faced by absolutely everyone are enjoyable simply because the audience is that much more engaged—and prepared.

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