On Monday we had an interesting seminar by Samory Kpotufe on nonparametric regression. Samory presented a method for choosing the smoothing parameter, locally, in nonparametric regression. The method is simple and intuitive: construct confidence intervals using many different values of the smoothing parameter. Choose the value at which the confidence intervals stop intersecting. He has a theorem that shows that the estimator adapts to the local dimension and to the local smoothness. Very cool. The idea is similar in spirit to ideas that have been developed by Oleg Lepski and Alex Goldenshluger. I am looking forward to seeing Samory’s paper.
On Wednesday we were fortunate to have another seminar by my old friend Christian Robert. Christian and I have not seen each other for a while so it was fun to have dinner and hang out. Christian spoke about ABC (approximate Bayesian computation). But really, ABC was just an excuse to talk about a very fundamental question: if you replace the data by a summary statistics (not sufficient), when will the Bayes factor be consistent? He presented sufficient conditions and then did some interesting examples. The conditions are rather technical but I don’t think this can be avoided. In our era of Big Data, this type of question will arise all the time (not just in approximate Bayesian computation) and so it was nice to see that Christian and his colleagues are working on this.
On a third, and unrelated note, I was watching CNN today. Someone named Roshini Raj (I believe she is a doctor at NYU) discussed a study from Harvard that showed that many foods, like pasta and red meat, are associated with depression. These reports drive me crazy. I have not looked at the study so I can’t comment on the study itself. But I had hoped that at least one anchor or the doctor would raise the obvious objection: this could be association without being causal. It did not occur to any of them to even raise this question. Instead, they immediately assume it is causal and started talking about the importance of avoiding pasta and red meat. I don’t find pasta or red meat depressing but I do find this kind of bad reporting depressing. Again, it is possible that the paper itself is careful about this; I don’t know. But the reporting sucks.