Archive for Markov chain Monte Carlo algorithm

j-ISBA Blackwell-Rosenbluth Award²⁶ [call reposted]

Posted in Statistics with tags , , , , , , , , , , , on May 15, 2026 by xi'an

Call for award nominations

Dear all,

It is with great pleasure that we announce the Blackwell-Rosenbluth Award by j-ISBA, a recently established award for junior researchers in different areas of Bayesian statistics. The award aims at recognizing outstanding junior Bayesian researchers based on their overall contribution to the field and to the community. There will be six winners in total who will be invited to present their work in two special events of the Junior Bayes Beyond the Borders (JB^3) webinar series and receive three years of free ISBA and j-ISBA membership.

ISBA proudly has a wide geographical diversity among its members. To encourage scientific exchange and strengthen research connections between geographies, three prizes will be awarded to researchers based in time zones UTC+0 to UTC+13 [e.g. Africa + Asia + Europe + Oceania] and three to those based in UTC-12 to UTC-1 [e.g. North America + South America]. We welcome nominations of junior researchers working in the broad spectrum of topics in Bayesian statistics, including but not limited to methods, theory, computation, machine learning, data science, biostatistics, econometrics, industrial statistics, environmental science, and software.

There will be two scientific committees: one representing UTC- and the other representing UTC+, each consisting of members from their respective regions based on their professional affiliations. These committees are tasked with evaluating candidates for the award. The UTC- committee will evaluate submissions from UTC+ and vice versa.

Why Blackwell-Rosenbluth

The award is named after David H. Blackwell and Arianna W. Rosenbluth for their groundbreaking works that lie at the foundation of modern Bayesian statistical theory and computation. They represent important role models for new researchers in Bayesian statistics.

David Harold Blackwell

Young Blackwell Born on April 24, 1919, Blackwell excelled in mathematics from an early age. He earned his doctoral degree from the University of Illinois at Urbana-Champaign under the supervision of Joseph L. Doob in 1941. He had a distinguished career, becoming a founding member in 1955 of the newly established Department of Statistics at University California, Berkeley. In 1965, he became the first African American to be elected member of the U.S. National Academy of Sciences and was awarded the John von Neumann Theory Prize in 1979. In addition to his seminal contributions to Bayesian inference, decision theory, game theory, sequential analysis and renewal theory, he also wrote one of the first textbooks in Bayesian statistics (Basic Statistics, McGraw-Hill, 1969).

Arianna Wright Rosenbluth

Young Rosenbluth Born on September 15, 1927, Arianna Wright Rosenbluth showed an affinity for sciences from early childhood. She completed her doctoral work under the supervision of a future Nobel Laureate, John Van Vleck, in 1949, making her the fifth woman to earn a Ph.D. in Physics from Harvard. Later, as a coauthor of the seminal 1953 paper introducing the Metropolis algorithm, Rosenbluth almost single-handedly implemented the algorithm on the MANIAC I hardware at the Los Alamos Scientific Laboratory. This made her the first person to ever implement the Markov chain Monte Carlo method when sophisticated programming tools were still years away, and the program had to be written in strings of 1’s and 0’s.

Eligibility and Application Procedure

Ph.D. students or early career researchers who obtained their PhD after January 1, 2021 are eligible for nomination. Candidates who were nominated in previous years may be nominated again if they received their Ph.D. after January 1, 2021. In exceptional cases, applicants who are more than five years past their Ph.D. may still be considered if they experienced a significant career break within five years of earning their degree (such as breaks due to illness, caring for a sick family member, pregnancy-related leave, or parental leave). Candidates may inquire about their eligibility, particularly if they have taken career breaks, by sending an email to jisba.section@gmail.com. A nomination may come from any ISBA member, including the nominee themselves. A nomination is to be submitted electronically and should contain:

  • Nominating letter in support of the candidate
  • CV of the candidate
  • One manuscript or alternate form of exposition (e.g. software documentation) of scientific work most representative of the nominee’s achievements; the submitted work should also be available as publication or in a public repository such as arXiv, bioRxiv, CRAN, Bioconductor or GitHub.

Timeline

Nominations for the 2026 award edition are now open! Deadline to submit is July 12, 2026

incoming mostly Monte Carlo [14 April, PariSanté campus]

Posted in pictures, Statistics, University life with tags , , , , , , , , , , , , , , , on April 9, 2026 by xi'an

The next Mostly Monte Carlo seminar will be this very Friday, 10/04/26, at PariSanté Campus. With Shiva Darshan and Pierre Monmarché speaking on the following topics:
15h: Shiva Darshan Maximal-reflection couplings on manifolds: some specific examples
Explicit Markovian couplings can be used to build Markov Chain Monte Carlo methods such unbiased MCMC or coupling based control variates. For sampling from probability measures supported on Euclidean space, one typically uses a synchronous coupling, a maximal-reflection coupling (also known as a discrete-time sticky coupling), or some variant of the two. For probability measures supported on Riemannian manifolds, the situation is less clear cut. While the Kendall-Cranston coupling of Brownian motions on manifolds has been successfully applied in theoretical works, it is ill-suited for building explicit algorithms. In this talk, we will discuss some of the obstacles to extending Euclidean maximal-reflection couplings to manifolds and present some special cases for which these obstacles can be easily overcome. With applications to Stereographic MCMC in mind, we detail particular couplings of random walks on the sphere.
16h: Pierre Monmarché A post-sampling reweighting method for multi-modal target measures
Even when the modes are identified and sampled locally with MCMC methods, a difficulty to sample multi-modal measures is to correctly estimate the relative probabilities of each of these modes, which requires to observe many transitions between them (which are rare events). We will present an approach based on variational inference which exploits the local samples, aiming only at estimating the relative weights between them. When the modes are well separated, this amount to some entropy estimations.

coupling-based approach to f-divergences diagnostics for MCMC

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , on October 27, 2025 by xi'an

Adrien Corenflos (University of Warwick) and Hai-Dang Dau (NUS) just arXived their paper on MCMC diagnostics that Adrien told me about last month, while in Warwick.

“This [f-divergence] bound is clearly suboptimal since it does not vary in t and does not take into account the mixing of the Markov chain. We present a scheme where the weights are ‘harmonized’ as the Markov chain progresses, reflecting its mixing through the notion of coupling.”

They start by opposing the classical ergodic average and embarrassingly parallel estimates obtained by N parallel chains culled of their B initial values, to couplings used in standard diagnoses. Opting for the parallel perspective, maybe rekindling the diagnostic war of the early 1990s! The evaluation tool in the paper is based on f-divergences, like the χ² divergence which naturally relates to the effective sample size when considering weighted atomic measures. When consistent, these weighted approximations produce upper bounds on the f-divergence, with exact convergence in case of independence.

In my opinion the most exciting part of the paper stands with the ability to modify these weights along MCMC iterations, since the naïve sequential importance sampling argument I also use in class keeps them constant! The trick is to (be able to) couple randomly chosen parallel chains, with the weights being averaged at each coupling event. The resulting algorithm preserves expectation (in the importance sampling sense) and consistency (in the particle sense). Furthermore, the f-divergence bound based on the weights can only decrease between iterations, which reminds me of interleaving. And exponential convergence of the weights to uniform ones (under the strong assumption of a uniformly lower bounded probability of coupling). The paper concludes with interesting remarks on perfect sampling, Rao-Blackwellisation, control variates, and backward sampling.

A long-standing gap exists between the theoretical analysis of Markov chain Monte Carlo convergence, which is often based on statistical divergences, and the diagnostics used in practice. We introduce the first general convergence diagnostics for Markov chain Monte Carlo based on any f χ² -divergence, allowing users to directly monitor, among others, the Kullback–Leibler and the divergences as well as the Hellinger and the total variation distances. Our first key contribution is a coupling-based ‘weight harmonization’ scheme that produces a direct, computable, and consistent weighting of interacting Markov chains with respect to their target distribution. The second key contribution is to show how such consistent weightings of empirical measures can be used to provide upper bounds to f -divergences in general. We prove that these bounds are guaranteed to tighten over time and converge to zero as the chains approach stationarity, providing a concrete diagnostic.

Advances in MCMC Methods [10-12 Dec, EURANDOM]

Posted in Statistics, Travel, University life with tags , , , , , , , , , on September 28, 2025 by xi'an

rethinking the ESS published!

Posted in Statistics with tags , , , , , , , , on May 3, 2022 by xi'an

Our paper Rethinking the Effective Sample Size, with Victor Elvira (the driving force behind the paper!) and Luca Martino, has now been published in the International Statistical Review! As discussed earlier on this blog, we wanted to re-evaluate the pros and cons of the effective sample size (ESS), as a tool assessing the quality [or lack thereof] of a Monte Carlo approximation. It is particularly exploited in the specific context of importance sampling. Following a 1992 construction by Augustine Kong, his approximation has been widely used in the last 25 years, in part due to its simplicity as a practical rule of thumb. However, we show in this paper that the assumptions made in the derivation of this approximation make it difficult to consider it as a reasonable approximation of the ESS. Note that this reevaluation does not cover the use of ESS for Markov chain Monte Carlo algorithms, although there would also be much to tell about it..!