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Round-robin (with Claude)

Posted in Books, Kids, R, Statistics, Wines with tags , , , , , , , , , , , , on August 15, 2026 by xi'an

A few days ago I had a coffee in Paris with my long-time friend (and former Statistics & Computing editor) Gilles Celeux, and he mentioned me stopping solving and posting maths puzzles like those weekly published by Le Monde. They have indeed vanished with the retirement of the authors, but Gilles added that the arrival of LLMs would have made the exercise moot. I disagreed as (i) the fun of solving the puzzle on my own  has not gone away and (ii) the pedagogical appeal of the puzzle and its resolution remains. As the next Fiddler puzzle arrived in my mailbox, my resolution was put to the test (contrariwise to the previous entry, which did not require massive computations):

The Fiddler League consists of two teams. Over a season, they play each other 162 times. Each team has an equal chance of winning each game, and the results of games are independent. Over the season, on average, how many games would you expect the team with the better record to have won?

I started on the wrong foot with E[X|X≥81] when X is Bin(162,½), equal to 85.77 (either directly or with a Normal approximation), which differs from my second thought, E[max(X,162-X)]=86.07 (either directly or with a Normal approximation), which is larger because of the reflection produced by max. While the first computation was manageable, the second one seemed to involve simulation and I caved in prompting Claude, which provided the answer along with the connection

E[max(X,162−X)]=E[X∣X≥81](1+p81​)−81p81​

After some expansion, the League boasts 30 teams. Over a season, each team plays each other team five times. (Each team plays a total of 145 games.) Again, each team has an equal chance of winning each game, and the results of games are independent. Over the season, on average, how many games would you expect the team with the best record to have won?

The best record is max(Xi) with each of the 30 Xi‘s a sum of 29 Yij and the Yij=5-Yji distributed as Bin(5,½). The Xi‘s are thus Bin (145,½) but dependent. While I could not figure out a closed form answer for the expectation, a direct Monte Carlo resolution is obviously feasible, with Claude (rather than me) running it over 400 million repetitions, but a 30 dimensional Normal approximation exploiting the correlation of 1/29 between the components leads to roughly 85 as the expected value. (Again computed by a Claudicant simulation.)

While the conclusion that the Normal approximation is pretty accurate with so many terms in the Binomial variates is quite unsurprising, Claude saves me coding time without ruining the puzzle altogether. (And Gemini made me aware that the name of the café where Gilles and I regularly meet, L’Écir, is an Auvergne noun for a local, dangerous, mountain blizzard! Thus linking the place to the foundation of the café by Auvergne expatriates…)

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the acceptance-complement method

Posted in Books, Statistics with tags , , , , , , on August 6, 2026 by xi'an

Last Saturday, while getting reacquainted with my home desk, I was delighted to spot a new arXival by Luc Devroye! Entitled the acceptance-complement method revisited, it discusses a variant of accept-reject method, where the target density f(·) is squeezed between two functions

0≤r(x)≤f(x)≤r(x)+q(x)

and can be simulated as the mixture

r(x)+(f(x)-r(x)),

assuming both r(·) and q(·) are proportional to densities that can easily be simulated. (With the additional constraint of q(·) having at most mass 1.) The nicest part is that the algorithm is always one-pass, as 

  1. generate Y~ q(y), U ~U(0,1)
  2. if Uq(Y)<f(Y)-r(Y), set X=Y
  3. else generate X~r(x)

with step 2 having two outcomes: either generate a realisation of [the density proportional to] f(·)-r(·) or generate an event of probability α when α is the mass [normalising constant] of r(·). This explains step 3 since the rejection of Y implies simulation from the second component of f(·). Brilliant! And Devroye derives a universal accept-complement algorithm for generic log-concave densities (that differs from Gilks & Wild, 1992.).

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Approximate Bayesian Computation with Statistical Distances for Model Selection [OWABI, 27 Nov]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on November 17, 2025 by xi'an

The next OWABI seminar is delivered by Clara Grazian (University of Sidney), who will talk about “Approximate Bayesian Computation with Statistical Distances for Model Selection” on Thursday 27 November at 11am UK time:

Abstract: Model selection is a key task in statistics, playing a critical role across various scientific disciplines. While no model can fully capture the complexities of a real-world data-generating process, identifying the model that best approximates it can provide valuable insights. Bayesian statistics offers a flexible framework for model selection by updating prior beliefs as new data becomes available, allowing for ongoing refinement of candidate models. This is typically achieved by calculating posterior probabilities, which quantify the support for each model given the observed data. However, in cases where likelihood functions are intractable, exact computation of these posterior probabilities becomes infeasible. Approximate Bayesian computation (ABC) has emerged as a likelihood-free method and it is traditionally used with summary statistics to reduce data dimensionality, however this often results in information loss difficult to quantify, particularly in model selection contexts. Recent advancements propose the use of full data approaches based on statistical distances, offering a promising alternative that bypasses the need for handcrafted summary statistics and can yield posterior approximations that more closely reflect the true posterior under suitable conditions. Despite these developments, full data ABC approaches have not yet been widely applied to model selection problems. This paper seeks to address this gap by investigating the performance of ABC with statistical distances in model selection. Through simulation studies and an application to toad movement models, this work explores whether full data approaches can overcome the limitations of summary statistic-based ABC for model choice.
Keywords: model choice, distance metrics, full data approaches
Reference: C. Grazian, Approximate Bayesian Computation with Statistical Distances for Model Selection, preprint at ArXiv:2410.21603, 2025

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exceptional OWABI web/sem’inar [19 June, BayesComp²⁵]

Posted in pictures, Statistics, Travel, Uncategorized, University life with tags , , , , , , , , , , , , , , on June 10, 2025 by xi'an


Exceptionally, the next One World Approximate Bayesian Inference (OWABI) Seminar will be hybrid as it is scheduled to take place during BayesComp 2025 in Singapore, on Thursday 19 June at 8pm Singapore time (1pm in Tórshavn) and two talks, one by Filippo Pagani on

Approximate Bayesian Fusion
Bayesian Fusion is a powerful approach that enables distributed inference while maintaining exactness. However, the approach is computationally expensive. In this work, we propose a novel method that incorporates numerical approximations to alleviate the most computationally expensive steps, thereby achieving substantial reductions in runtime. Our approach retains the flexibility to approximate the target posterior distribution to an arbitrary degree of accuracy, and is scalable with respect to both the size of the dataset and the number of computational cores. Our method offers a practical and efficient alternative for large-scale Bayesian inference in distributed environments.
and one by Maurizio Filippone on
GANs Secretly Perform Approximate Bayesian Model Selection
Generative Adversarial Networks (GANs) are popular models achieving impressive performance in various generative modeling tasks. In this work, we aim at explaining the undeniable success of GANs by interpreting them as probabilistic generative models. In this view, GANs transform a distribution over latent variables Z into a distribution over inputs X through a function parameterized by a neural network, which is usually referred to as the generator. This probabilistic interpretation enables us to cast the GAN adversarial-style optimization as a proxy for marginal likelihood optimization. More specifically, it is possible to show that marginal likelihood maximization with respect to model parameters is equivalent to the minimization of the Kullback-Leibler (KL) divergence between the true data generating distribution and the one modeled by the GAN. By replacing the KL divergence with other divergences and integral probability metrics we obtain popular variants of GANs such as f-GANs, Wasserstein-GANs, and Maximum Mean Discrepancy (MMD)-GANs. This connection has profound implications because of the desirable properties associated with marginal likelihood optimization, such as (i) lack of overfitting, which explains the success of GANs, and (ii) allowing for model selection, which opens to the possibility of obtaining parsimonious generators through architecture search.

These talks will be delivered on-site and on-line, as a Zoom visio-conference.

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next OWABI webinar [24 April]

Posted in pictures, Statistics, Uncategorized, University life with tags , , , , , , , , , , , , on April 16, 2025 by xi'an


The next One World Approximate Bayesian Inference (OWABI) Seminar is scheduled on Thursday the 24th of April at 11am UK time (12am CET) with the speaker being Ayush Bharti (Aalto University), who will talk about

“Cost-aware simulation-based inference “

Abstract: Simulation-based inference (SBI) is the preferred framework for estimating parameters of intractable models in science and engineering. A significant challenge in this context is the large computational cost of simulating data from complex models, and the fact that this cost often depends on parameter values. We therefore propose cost-aware SBI methods which can significantly reduce the cost of existing sampling-based SBI methods, such as neural SBI and approximate Bayesian computation. This is achieved through a combination of rejection and self-normalised importance sampling, which significantly reduces the number of expensive simulations needed. Our approach is studied extensively on models from epidemiology to telecommunications engineering, where we obtain significant reductions in the overall cost of inference. .

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