Archive for Bayesian bootstrap

Seminal ideas and controversies in Statistics [book review]

Posted in Books, Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on May 24, 2025 by xi'an

CRC Press sent CHANCE this book for review. Since the topic was of clear interest to me, with an author who significantly contributed to the field—my only recollection meeting Roderick Little was during the Australian Statistical Conference in Adelaïde, in 2012, at the start of my Oz 2012 Tour!—, I took the opportunity of the nearest weekend to browse through Seminal ideas and controversies in Statistics. I like very much the idea of selecting a dozen key papers in the history of Statistics and of discussing why. In fact, this reminded me of my classics seminar, which lasted the few years I was 100% in charge of the Master program in Dauphine (and which I hope I could restart!). Checking the list of the papers I then suggested my students, I see some overlap with 9 papers out of the 15 groups. (I also remember Steve Fienberg making suggestions for that list, while he was spending a sabbatical in Paris at CREST.) Given that community of focus and purpose, and contrary to my wont, I have really very little of substance to criticize or wish about the book. The less when reading the following

“On a personal note, I met Yates [author of a 1984 paper on tests for 2×2 contingency tables discussing the relevance of conditioning on one or both margins], a charming man, when I was a young graduate student who knew next to nothing about statistics; we discussed the joys of traversing the Cuillin Ridge in Skye.”

since completing that ridge remains high in my mountain-climbing bucket-list! (Possibly next year, since we are running an ICMS workshop on the Island.)

The first paper in the series is more than a foundational paper since (The) Fisher’s 1922 paper is about creating (almost) ex nihilo the field of (modern) mathematical statistics. I don’t know if there is any equivalence in other scientific disciplines of such an impact (and of such a man)… Roderick Little manages to convincingly engage with Fisher’s dismissive views on (not yet called) Bayesian analysis, although, to the latter’s defence, the formalisation of Bayesian inference at that time had not yet emerged. The second chapter is discussing Yates’ 1984 paper on tests for 2×2 contingency tables that he wrote 50 years after writing the original one in the first volume of JRSS. Roderick Little adds a detailed Bayesian analysis with the three standard reference priors, Jeffreys’ version proving quite close to Fisher’s exact test (conditional on both margins). The third chapter is aiming at the generic challenge of hypothesis testing, from the well-known opposition between Fisher and Neyman (both on the cover), to questioning the sanity of hard-set thresholds (with a mention of our American Statistician call to abandon (shi)p!). The later (thus) refers to the recent literature on the replicability crisis and the now famous ASA statement on p-values by Ron Wasserstein and Nicole Lazar, analysed in the chapter. But I would have like to read another full section on alternatives to hypothesis testing. While now a niche interest (imho), Fisher’s attempt at creating a posterior distribution without a prior, aka fiducial inference, is discussed in Chapter 4 with the Behrens-Fisher problem as the illustrating example. The chapter feels rather anticlimactic, with the comparison relying on the (Malay) Ghosh and Kim (2001) simulation results.

Birnbaum’s (1962) likelihood principle is the topic of Chapter 5 (and I cannot remember any of my students choosing this paper over the years, although there was at least one). Roderick Little recalls some sentences from the JASA discussion as an appetiser, a reminder of the time when these discussions could turn in scathing attacks. The chapter contains excerpts from Berger and Wolpert (1988)—which they were writing while I was spending a year at Purdue and which I have always recommended to my PhD students, albeit not for the classic seminar. It then moves to the controversies that surround this principle since its inception, in particular those accumulated by Deborah Mayo (also on the cover) as reported on the ‘Og. In the recent years, I have become less excited about the LP, in part due to the imprecision in its statement, which opens the door to conflicting interpretations. And in part due to the scarcity of models with non-trivial sufficient statistics. (I am also wondering if the sufficiency issue we highlighted in our ABC model choice criticism does relate to the mixture example at the end of the chapter.)

The next chapter is one all for compromise, through the calibrated Bayes perspective that credible statements should be close to confidence statements in the long run. Which I remember him presenting at ASC 2012. The concept is found in the very 1984 paper by Don Rubin (also on the cover) that contains the concept behind Approximate Bayesian Computation (ABC). And the chapter proceeds by listing strengths and weaknesses of frequentist and Bayesian perspectives, towards a fusion of both., e.g. though posterior predictive checks.

While the choice of a (general public) paper from Scientific American may sound surprising in Chapter 7, with Efron’s (on the cover) and Morris’ 1977 Stein’s paradox, I cannot but applaud, the more because this was the first paper I read when starting my PhD on the James-Stein estimators. Although this may sound like happening eons ago, the James and Stein (1961) paper—which is my age!—”created a considerable backlash” by toppling unbiasedness from its pedestal and exhibiting a paradox that 1+1+1≠3… Which Little reinterprets via a random effect (or Bayesian hierarchical) model. (And a chapter where I learned that Little’s father was a journalist, a characteristic he shared with Bruce Lindsay, as I found at Blonde, Glasgow, during an ICMS workshop). Relatedly, the next chapter is about the “57 varieties [of regression] paper” by Demptster, Schatzoff and Wermuth (1977). Apparently connected with Heinz 57 varieties of pickles. The paper considers Stein and ridge and variable selections versions for variable selection. The chapter also covers (Bayesian) Lasso and BART, as well as a brief all too brief mention of Spike & Slab priors—with my friend Veronika Ročková missing from the authors’ index!—,  but I was expecting from the title other, robust, forms of regression like L¹ regression and econometrics digressions. Chapter 10 can however been seen as a proxy since covering generalized estimating equations from a 1986 Biometrika paper of Liang and Zeger, with no Bayesian aspect (and an expected appearance of Communications in Statistics B).

Chapter 9 covers the almost immediately classic 1995 paper of Benjamini and Hochbeg on multiple regressions (that Series B turned into a discussion paper ten years later!). Although it spends more time on Berry’s (2012) recommendations than on FDR. The computational Chapter 11 brings together Efron’s (1979) bootstrap [with his picture on the cover] and MCMC, represented by the founding paper of Gelfand and Smith (1990, if mistakenly set in 1988 on p140). A bit of a strange mix imho as the former is more inferential than computational. And not giving the EM algorithm that much space. And not questioning MCMC methods as a good proxy to posterior distributions. Tukey’s Future of Data Analysis (as founding exploratory data analysis) and Breiman’s Two cultures (as launching statistical machine learning) meet in Chapter 12. (With a reminder that the latter invokes Occam’s razor—which may not be that appropriate for hugely overparameterised machine learning black boxes—and…the Rashomon principle! Meaning that distinct models may all fit the same data. Let me nitpickingly add the reference to Ryûnosuke Akutagawa as the author of Rashômon and other stories that Kurosawa adapted in his splendid movie). The chapter contains critical remarks from David Cox, Brad Efron, David Bickel, and Andrew Gelman, with a further section on Little’s view on modelling.

The last three chapters are on design and sampling, in connection with Little’s (and Rubin’s) works in the area. With a 1934 paper of Neyman (whose picture on the cover could have been chosen differently, albeit no fault of Neyman [or of Little!] that his toothbrush style of moustache dramatically got out of fashion!). With a return to calibrated Bayes and a reminiscence of Little’s time at the World Fertility Survey but (apparently) no mention of the probabilistic aspects of modern censuses (that saw my friends Steve Fienberg on the one side and Larry Brown and Marty Wells on the other side argue for and against it!), again relating to the reliance on statistical models. Chapter 14 relates randomized clinical trials to causality, which makes a (worthy) appearance there. Roderick Little also makes a clear case there against the retracted study linking vaccines and autism, a call that will unlikely not reach the current Trump administration and its Secretary of Health.

The book concludes with a list of twenty style and grammar suggestions for improved writing.

As should be crystal-clear from the above, I quite enjoyed the book and would definitely use its reading list in a graduate course whenever the opportunity arises. Once again, some choices are more personal to the author than others, and I would have place more emphasis on the fantastic Dawid, Stone and Zidek (1973)—with Jim Zidek also missing from the author index—, but all make sense in a walk through statistical classics. Let me however regret the absence therein of major actors like, e.g., D. Blackwell, C.R. Rao,  or G. Wahba (except in a stylistic example p199), two of whom were awarded the International Prize in Statistics.

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE.]

IISA 2024

Posted in Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , on January 12, 2025 by xi'an

The IISA 2024 conference was held at the Cochin University of Science and Technology (CUSAT), where talks and posters took place. Among the sessions I attended, I attended a  talk on colliding random walks that made three or more  impossible in the limit, missed the only privacy talk that I could have attended by Vinayak Rao for indulging into a dawnish swimming session in the very decent hotel pool. In the first session I organised, loosely connected with BNP, Antonietta Mira presented a recent work on predicting EU carbon compensation rates, using a information imbalance rank substitute to correlation that could prove quite interesting in privacy settings, albeit no invariant to reparameterisations (with potential connections with Wasserstein distances), Sonia Petrone gave an overview on her substantial amount of work on empirical Bayes in Bayes (EBIB), making me wonder at natural ABC or EM ways to bypass the computation of the empirical Bayes hyperparameter computation (but also on measuring the overfitting degree of EBIB-ing), maybe exploiting the representation of the marginal as an average of predictive, and Debdeep Pati argued towards an interpretable and robust ML, using for estimation divergence a mixture of two KL’s that is remindful of GANs (as well as of Lasso and exponentially tilted empirical likelihood à la Chib & al.), implemented by a form of Bbootstrap. Plus enjoying a locally flavoured acronym, namely BETEL.
The second session I organised was centred on Bayesian computations, with both Sid Chib and Ritabrata Dutta (U Warwick) presenting a Bayesian modelling of difference-in-difference models in clinical trials and several works on (score based) generalized Bayes models with Shreya Roy (U Warwick), who further won a poster prize at IISA 2024. I terminated the session with a talk on our insufficient Gibbs sampler, which connected with some aspects of both Sid’s and Rito’s talks.

As in earlier editions of IISA I attended, the local organisation was most enjoyable, from supportive staff and students, relaxed atmosphere, easy commutes, heaps of great food, and unlimited chai! Plus meeting and listening to participants I had met in these earlier editions. Looking forward the 2026 edition!

Nice meeting!

Posted in pictures, R, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , on December 18, 2024 by xi'an

The ICSDS 2024 meeting in Nice is quite impressive and not primarily because it is in Nice under a beautiful December sun. As other (numerous) IMS meetings I attended (since the initial one in Uppsala in 1990!), the program is of high quality and along topics that are currently moving fast or emerging. From the sessions I attended, e-values are strongly represented, although it remains unclear to me why they should constitute a major departure from p-values, as they stick to hypothesis testing, Type I error, power, and the whole paraphernalia of Neyman-Pearson formalism. If I manage to attend a BIRS workshop on the subject next Summer, I may manage to get a better e-derstanding!The MCMC (only!) session included a presentation by Guanyang Wang that generalised different approximate MCMC schemes into a unified one. And one by Filippo Ascolani on Gibbs beating the competition! I also attended the Bayesian prediction session, where my friends Sonia Petrone and Chris Holmes have presentations on their respective Series B papers. I discussed both on the ‘Og, on 15 March 2023 and 07 November 2022, respectively. This time, I found that both talks had a Bayesian bootstrap flavour, which is not surprising when considering the non-parametric nature of the approach. And they left me wondering at it being protected from overfitting.
My only plenary session was Cynthia Dwork’s on outcome indistinguishability, which, while related to the privacy topics I was topic, remained somewhat obscure as to its purpose. Meaning I have to get through the paper to get a more holistic perspective.
Of course, Nice in Winter is a very nice place, with the waterfront available for running an uninterrupted 15km as we found out with Jérémie Houssineau (at a brisk 4’09” pace I had not planned before starting!) and the sea all for myself (for a dozen minutes before losing digits!). Unfortunately I had to skip the final day due to examinations of the Paris Dauphine MASH master. And miss Stan receiving a student award. But I am looking forward the next iterations of ICSDS. (Not including Copenhagen, Madrid and many many other places in 2025, since ICSDS seemed a most common name for conferences, some presumably predatory! The true location is Sevilla, to keep up with the Mediterranean theme of ICSDS!)

ABC in Lapland²

Posted in Mountains, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , on March 16, 2023 by xi'an

On the second day of our workshop, Aki Vehtari gave a short talk about his recent works on speed up post processing by importance sampling a simulation of an imprecise version of the likelihood until the desired precision is attained, importance corrected by Pareto smoothing¹⁵. A very interesting foray into the meaning of practical models and the hard constraints on computer precision. Grégoire Clarté (formerly a PhD student of ours at Dauphine) stayed on a similar ground of using sparse GP versions of the likelihood and post processing by VB²³ then stir and repeat!

Riccardo Corradin did model-based clustering when the nonparametric mixture kernel is missing a normalizing constant, using ABC with a Wasserstein distance and an adaptive proposal, with some flavour of ABC-Gibbs (and no issue of label switching since this is clustering). Mixtures of g&k models, yay! Tommaso Rigon reconsidered clustering via a (generalised Bayes à la Bissiri et al.) discrepancy measure rather than a true model, summing over all clusters and observations a discrepancy between said observation and said cluster. Very neat if possibly costly since involving distances to clusters or within clusters. Although she considered post-processing and Bayesian bootstrap, Judith (formerly [?] Dauphine)  acknowledged that she somewhat drifted from the theme of the workshop by considering BvM theorems for functionals of unknown functions, with a form of Laplace correction. (Enjoying Lapland so much that I though “Lap” in Judith’s talk was for Lapland rather than Laplace!!!) And applications to causality.

After the (X country skiing) break, Lorenzo Pacchiardi presented his adversarial approach to ABC, differing from Ramesh et al. (2022) by the use of scoring rule minimisation, where unbiased estimators of gradients are available, Ayush Bharti argued for involving experts in selecting the summary statistics, esp. for misspecified models, and Ulpu Remes presented a Jensen-Shanon divergence for selecting models likelihood-freely²², using a test statistic as summary statistic..

Sam Duffield made a case for generalised Bayesian inference in correcting errors in quantum computers, Joshua Bon went back to scoring rules for correcting the ABC approximation, with an importance step, while Trevor Campbell, Iuri Marocco and Hector McKimm nicely concluded the workshop with lightning-fast talks in place of the cancelled poster session. Great workshop, in my most objective opinion, with new directions!

ABC in Lapland

Posted in Mountains, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , on March 15, 2023 by xi'an

Greetings from Levi, Lapland! Sonia Petrone beautifully started the ABC workshop with a (the!) plenary Sunday night talk on quasi-Bayes in the spirit of both Fortini & Petrone (2020) and the more recent Fong, Holmes, and Walker (2023). The talk got me puzzled by wondering the nature of convergence, in that it happens no matter what the underlying distribution (or lack thereof) of the data is, in that, even without any exchangeability structure, the predictive is converging. The quasi stems from a connection with the historical Smith and Markov (1978) sequential update approximation for the posterior attached with mixtures of distributions. Which itself relates to both Dirichlet posterior updates and Bayesian bootstrap à la Newton & Raftery. Appropriate link when the convergence seems to stem from the sequence of predictives instead of the underlying distribution, if any, pulling Bayes by its own bootstrap…! Chris Holmes also talked the next day about this approach, esp. about a Bayesian approach to causality that does not require counterfactuals, in connection with a recent arXival of his (on my reading list).

Carlo Alberto presented both his 2014 SABC (simulated annealing) algorithm with a neat idea of reducing waste in the tempering schedule and a recent summary selection approach based on an auto-encoder function of both y and noise to reduce to sufficient statistic. A similar idea was found in Yannik Schälte’s talk (slide above). Who was returning to Richard Wiilkinson’s exact ABC¹³ with adaptive sequential generator, also linking to simulated annealing and ABC-SMC¹² to the rescue. Notion of amortized inference. Seemingly approximating data y with NN and then learn parameter by a normalising flow.

David Frazier talked on Q-posterior²³ approach, based on Fisher’s identity, for approximating score function, which first seemed to require some exponential family structure on a completed model (but does not, after discussing with David!), Jack Jewson on beta divergence priors²³ for uncertainty on likelihoods, better than KLD divergence on e-contamination situations, any impact on ABC? Masahiro Fujisawa back to outliers impact on ABC, again with e-contaminations (with me wondering at the impact of outliers on NN estimation).

In the afternoon session (due to two last minute cancellations, we skipped (or [MCMC] skied) one afternoon session, which coincided with a bright and crispy day, how convenient! ), Massi Tamborino (U of Warwick) FitzHugh-Nagumo process, with impossibilities to solve the inference problem differently, for instance Euler-Maruyama does not always work, numerical schemes are inducing a bias. Back to ABC with the hunt for a summary that get rid of the noise, as in Carlo Alberto’s work. Yuexi Wang talked about her works on adversarial ABC inspired from GANs. Another instance where noise is used as input. True data not used in training? Imke Botha discussed an improvement to ensemble Kalman inversion which, while biased, gains over both regular SMC timewise and ensemble Kalman inversion in precision, and Chaya Weerasinghe focussed on Bayesian forecasting in state space models under model misspecification, via approximate Bayesian computation, using an auxiliary model to produce summary statistics as in indirect inference.