Following our arXival on the new version of our HPD based Gelfand & Dey estimator of evidence, I got pointed at Wang et al. (2018), which I had forgotten I had read at the time (as testified by an ‘Og entry). Reading my own comments, I concur (with myself¹⁸!) that the method is not massively compelling since it requires a partition set that is strongly related with the targeted integral. The above illustration for a mixture, that is for a pseudo posterior that is a mixture with two Gaussian components with known variance, also shows (in reverse) the curse of dimension and the need for finely tuned partitions. Said partition corresponding to the myriad of sets on the rhs. With such a degree of partitioning, Riemann integration should also produce perfect estimate, as shown by the zero error in the resulting estimator (Table 4).
Archive for Monte Carlo Statistical Methods
estimating evidence redux
Posted in Books, Statistics, University life with tags Bayesian Analysis, curse of dimensionality, estimating a constant, evidence, harmonic mean estimator, HPD region, importance sampling, marginal likelihood, Monte Carlo Statistical Methods on November 21, 2025 by xi'anfinite variance goals
Posted in Books, Statistics, Travel, University life with tags ChatGPT, control variates, importance sampling, infinite variance estimators, MathJax, Monte Carlo Statistical Methods, Pareto smoothed importance sampling, plugin, University of Warwick, Wordpress, xianblog on November 8, 2025 by xi'an
During Johan Seger’s seminar in Warwick, on the control variate improvements he developed with Rémi Leluc (which PhD thesis committee I joined), Aymeric Dieuleveut, François Portier, and Aigerim Zhuman, I started wondering at whether or not a control variate could turn an infinite variance Monte Carlo estimate into a finite variance one. And asked… ChatGPT about it, with the above reply that is correct if not practical in the least since the example provided therein was reverse-engineering an infinite variance rv into a sum of an infinite variance rv considered as the control variate and a finite variance rv. As summarised below. In practice, this would mean replacing the integrand of interest with a much simpler integrand that shares the same asymptotic behaviour, not an easy task! (As an aside, I found out that enabling MathJax on this ‘Og would cost me $40 a month!)
5. Summary
✅ Theoretical possibility:
Yes — control variates can make an infinite-variance estimator finite, but only if the control’s sample path shares the same tail driver and its expectation is known.infinite variance rv
In real-world Monte Carlo, when X is heavy-tailed, you usually:
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Split X = Y + (X-Y), where Y has known expectation and similar tails,
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Use Y as control variate, and
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Possibly combine with truncation, conditional expectation, or importance sampling for stability.
mostly Monte Carlo, November
Posted in pictures, Statistics, Travel, University life with tags coupling, f-divergence, MCMC, Monte Carlo Statistical Methods, Paris Sciences et Lettres, PariSanté campus, PSL, seminar, Università Bocconi, Université Paris Dauphine, University of Warwick, variational inference on November 7, 2025 by xi'an
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Omiros Papaspiliopoulos (Università Bocconi): Bilinear mixed models and variational inference
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Adrien Corenflos (University of Warwick): A coupling-based approach to f-divergences diagnostics for Markov chain Monte Carlo [recently discussed on the ‘Og]
mostly Monte Carlo, the return²⁵
Posted in pictures, Statistics, University life with tags ABC, CEREMADE, COVID-19, differential privacy, MCMC, Monte Carlo Statistical Methods, Paris Sciences et Lettres, PariSanté campus, permABC, permutations, PSL, seminar, SIR, Université Paris Dauphine, Wasserstein distance on October 9, 2025 by xi'an
Our local Mostly (and monthly) Monte Carlo seminar is back for a new academic year, now organized by Antoine Luciano and Timothy Johnston. The first session will take place at the PariSanté Campus on Friday 17 October 2025 (3:00pm, room 07), with the organisers opening the dance, with two talks:
3pm Timothy Johnston (CEREMADE, Université Paris Dauphine–PSL): Differential Privacy of Markov Chains
Joint work with Andrea Bertazzi, Alain Durmus and Gareth Roberts
In this talk we shall discuss differential privacy, a framework for quantifying the extent to which a random output depends on the information used to produce it. After introducing several related definition of differential privacy, we shall discuss techniques used to show the differential privacy of both trajectories and single draws from Markov Chains. In doing so we shall touch on a perturbation technique which allows for Wasserstein type bounds to be converted into stronger distances like the KL and Renyi divergence.
4pm Antoine Luciano (CEREMADE, Université Paris Dauphine–PSL): Permutations accelerate Approximate Bayesian Computation
Joint work with Charly Andral, Christian P. Robert and Robin J. Ryder
Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in hierarchical or high-dimensional models. In this paper, we introduce permABC, a new ABC framework designed for settings with both global and local parameters, where observations are grouped into exchangeable compartments. Building upon the Sequential Monte Carlo ABC (ABC-SMC) framework, permABC exploits the exchangeability of compartments through permutation-based matching, significantly improving computational efficiency. We then develop two further, complementary sequential strategies: Over Sampling, which facilitates early-stage acceptance by temporarily increasing the number of simulated compartments, and Under Matching, which relaxes the acceptance condition by matching only subsets of the data. These techniques allow for robust and scalable inference even in high-dimensional regimes. Through synthetic and real-world experiments – including a hierarchical Susceptible-Infectious-Recover model of the early COVID-19 epidemic across 94 French departments – we demonstrate the practical gains in accuracy and efficiency achieved by our approach.
Advances in MCMC Methods [10-12 Dec, EURANDOM]
Posted in Statistics, Travel, University life with tags ABC-MCMC, computational physics, Eindhoven, Eurandom, inverse problems, machine learning, Markov chain Monte Carlo algorithm, Monte Carlo Statistical Methods, the Netherlands, workshop on September 28, 2025 by xi'an
