The MLE conjecture, the IMS bulletin and Science

The latest issue of the IMS bulletin contains a letter in which a reader, Anirban DasGupta from Purdue University, lays out his thoughts regarding Ning-Zhong Shi’s MLE conjecture. Evidently, DasGupta’s comments were considered of higher relevance than my own letter to the bulletin’s editors regarding the conjecture, a letter which described the same counter-example to the conjecture that appears in the post linked above.

In his letter, Prof. DasGupta does not actually provide either a proof or a counter-example to Shi’s conjecture. Instead he reports that his hopes to find a “quick counterexample” were dashed when he discovered that, beyond the obvious case of the MLE for the expectation of a set of IID normals, “the conjecture happens to be true in a few slightly unusual examples” and concludes that “[t]he conjecture is probably true in many examples on a case-by-case basis, but would be nearly impossible to prove in general.” The bulk of the letter then breezes through a few matters tangentially connected to Shi’s conjecture: sub-martingales, U-statistics and Bayesian estimates and – of course – contains a couple of citations.

Working within the model which sees Science as a rational activity, the editorial decision to publish a lengthy, inconclusive letter regarding the conjecture rather than a simple counter-example would seem perplexing as it runs contrary to the supposed preference of Science for short and clear answers to long and equivocal ones. However, when viewing Science as primarily a political activity, this editorial decision joins the original decision to publish Shi’s conjecture in the first place as no more than an indication that Prof. Shi has some powerful friends.

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