To recap, I thus attended the BIRS-CMI workshop 25w5482 at the Chennai Mathematical Institute, Navalur, Tamil Nadu, in early July, for being intrigued by the developments around the concept. And enjoyed the week, from partaking in the company of friendly and enthusiastic academics to the exposure of new views and concepts, mostly remote from mine’s. Recall that an e-value attached to an hypothesis H described as a collection of distributions is a non-negative random variable E with expectation less than 1 for E~Q and all Q ∈ H. When a stopping rule is involved, the e-value is extended into an e-process. (Beyond Aaditya Ramdas’ E-book, Ruodu Wang also wrote a “tiny” review.) Aaditya Ramdas recalled in his introduction of the workshop that e-values are fundamentally equivalent to p-values and confidence intervals. And that a confidence sequence is a sequence of confidence intervals that contains the true value for all time steps t’s with a probability of at least 1-α.
The talks reflected a general belief in α levels and in Neyman-Pearsonian likelihood ratio optimality in simple vs simple settings, considering extension for sequential analysis settings, anytime inference, universality under general alternatives, and connections with FDRs, incl. Benjamini & Hochberg solution, but pointed out a lack of middle ground between frequentists and Bayesians.
“e-values have a clear interpretation in terms of betting and are closely related to likelihood ratios and other Bayes factor. At the same time, e–values do not require prior distributions conditional on the null and alternative hypotheses”
Although David R. Bickel attempted a Bayesian version, using a marginal likelihood ratio within betting settings, that is an incoming American Statistician paper. I may have being missing some aspects due to a lack of sleep the night before (!), but I find the attempt resulting in a fairly unusual vision of Bayesian testing as either not depending on any parameter or on the opposite using a family of priors. I did not understand either the “criticism” that the predictive depends on the prior and felt that this representation was bending in a rather onsiderable way the Bayesian perspective towards achieving a certain degree of agreement with p– and e-value notions, to conclude that the Bayes factor is an e-value. (As an aside, this may be the first paper that cited our critical review of Aitkin! Similarly, Shubhada Agrawal mentioned Roger Farrell in his talk, with whom we wrote a complete class Annals paper in the late 1980’s.) Nikos Ignatiadis also explored Empirical Bayes e-values, while Ben Chugg gave a presentation (constrained) admissibility, albeit under type-I error constraints that makes Bayes infeasible and using Neyman-Pearsonian loss functions. On the last day, Peter Grünwald tried for some BFF cohesion with openings on e-posteriors, treating hypothesis testing losses symmetrically, defining it as an inverse of e-values but incorporating pseudo-posteriors of many flavours like confidence, inferential, and fiducial distributions. He also mentioned a Savage-Dickey version while using an arbitrary prior, which is also an e-value, but with upper & lower meanings, again with measure issues
Given the hosting of the workshop in the Chennai Mathematical Institute, which is quite far from the centre of town (much closer to Mahabalipuram!), I did not visit Chennai but enjoyed the South Indian cuisine (albeit missing some fierceness in the spices!) and local fruits from street stands, if being sorry I could not find cocoa pods from nearby Kerala.
