Archive for Chennai Mathematical Institute
fishing boats, Mahabalipuram [jatp]
Posted in pictures, Travel, University life with tags Bay of Bengal, BIRS-CMI, Chengalpet District, Chennai, Chennai Mathematical Institute, Dravidian culture, fishermen, fishing, group tour, India, jatp, Mahabalipuram, Mahabharata, Mamallapuram, Pacific Ocean, Tamil Nadu on August 19, 2025 by xi'an
on stopping rules
Posted in Books, Statistics with tags 25w5482, Bayesian testing, BIRS-CMI, Chennai, Chennai Mathematical Institute, e-values, evidence, game theory, inference, Likelihood Principle, Madras, martingales, p-values, sequential analysis, stopping rule, Tamil Nadu, The American Statistician, workshop on August 3, 2025 by xi'an
The workshop in Chennai and its focus on sequential procedures made me realise (among other things) I had never read Cornfield’s 1966 TAS paper on sequential testing and the likelihood principle:
“By sequential analysis I mean any form of analysis in which the conclusion depends not only on the data, but also on the stopping rule.”
Written with little maths and formalism, this paper argues that keeping a fixed critical level amounts to keeping a fixed amount of evidence. Hence constituting an early critique of p-values even though not expressed in such terms. The part of the paper related with the likelihood principle does not address testing or evidence in a Bayesian way. As a side (late awakening) remark, iid observations in sequential settings are not longer independent, conditional on the stopping rule realisation N=n, since they are constrained by the fact that the stopping rule realisation is n and not n-1, n-2, … For a short while, I thought it was in turn impacting the distribution of any “sufficient” statistic one may propose, with a normalising constant that depends on the unknown parameter and hence cannot be neglected. Over all those years, I had never though of the modification of sufficiency characteristics in such contexts. But in fine the pair made of the value of the stopping rule and of the unsequential sufficient statistics proves enough. And the normalisation constant is the probability that the stopping rule.. stops!, which is equal to one! For the same short while, I was then wondering that the stopping rule principle!
“my second line of argument that there is a reasonable alternative explication of the idea of inference and one which leads to the rejection of sequential analysis. This explication is provided by the likelihood principle—which states that all observations leading to the same likelihood function should lead to the same conclusion.”
I thus went back to the fundamentals (!), namely [freely available] Bernardo’s and Smith’s Section 5.1.4 (reproduced in EJ’s Stopping rule appendix, also citing Cornfield at length), where the likelihood is properly defined by the joint density of the stopping rule τ and the attached sample at their realised values. And failing in the end (and a discussion with Judith)nto spot a missing normalisation constant.
e-values in Chennai
Posted in Books, pictures, Running, Statistics, Travel, University life with tags Abraham Wald, admissibility, Bayes factors, Bayesian hypothesis testing, Benjamini, BIRSCMI, Chennai, Chennai Mathematical Institute, complete class theorems, confidence sequence, Dickey-Savage ratio, e-values, empirical Bayes methods, FDRs, Hochberg, Neyman-Pearson tests, p-values, sequential testing, south Indian cuisine, Tamil Nadu on July 23, 2025 by xi'an
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.
a passage to India [book review]
Posted in Books, Mountains, pictures, Travel with tags book review, Britain, British Raj, Chennai, Chennai Mathematical Institute, E.M. Forster, imperialism, India, Indian independence, Penguin Classics, religions, systemic racism, tea, Victorian society, Walt Whitman on July 16, 2025 by xi'an
Feeling I had missed a classic of English literature and curious to see Forster’s views on colonial India, I started this book on a plane to India and finished it before I returned. The writing style is excellent, the characters are complex and, for the most multifaceted, the setting is inspired by Forster’s visits to India and hence realistic, the story timeline is well-set, for the most (ie except for the last part), and the scenario is engaging and realistic, but, obviously, what makes the book a masterpiece is its depiction of the British Raj from many perspectives, from British enforcers of its colonialism to British critics of said colonialism, to Indians trained in Britain, to completely local Indians, with the clash of multiple cultures and religions. Victorian prudery mixes with racial prejudices, resentment against discriminations leads to early (?) germs of fighting for independence, and the characteristic reaction of such a discriminatory and racist society to a claim of sexual impropriety on a British woman from a native man. This central event of the book is brought in both very subtly and unexpectedly (for those like me who had no initial idea of the story), with an equally subtle uncertainty about what really happened that remains till the end. If anything, the book may be delivering a pessimistic message on the impossible friendship between individuals from the ruling and oppressed groups, despite it being scandalous at the time for even suggesting such a friendship was conceivable. (The attached cover of the Penguin Classic edition is amazingly close to the excursion episode!)
Pandava Rathas, Mahabalipuram [jatp]
Posted in pictures, Travel with tags Bay of Bengal, BIRS-CMI, Buddhism, bulls, Chengalpet District, Chennai, Chennai Mathematical Institute, Dravidian culture, group tour, Hindu temples, Hinduism, India, jatp, Mahabalipuram, Mahabharata, Mamallapuram, monolith, Pacific Ocean, Pallava dynasty, Pancha Rathas, Pandava Rathas, Tamil Nadu, Unesco World Heritage List on July 6, 2025 by xi'an
