The next mostly MCMC seminar is actually happening today and (darn!) I forgot to advertise it! For those who can still make it, it will take place at 3PM (CEST) at the PariSanté Campus (in Room 08). The talks are by
This special issue of Statistical Science is devoted to the future of Bayesian computational statistics, from several perspectives. It involves a large group of researchers who contributed to collective articles, bringing their own perspectives and research interests into these surveys. Somewhat paradoxically, it starts with the past—and a conference on a Gold Coast beach. Martin, Frazier, and Robert first submitted a survey on the history of Bayesian computation, written after Gael Martin delivered a plenary lecture at Bayes on the Beach, a conference held in November 2017 in Surfers Paradise, Gold Coast, Queensland, and organised by Bayesian Research and Applications Group (BRAG), the Bayesian research group headed by Kerrie Mengersen at the Queensland University of Technology (QUT). Following a first round of reviews, this paper got split into two separate articles, Computing Bayes: From Then ‘Til Now , retracing some of the history of Bayesian computation, and Approximating Bayes in the 21st Century, which is both a survey and a prospective on the directions and trends of approximate Bayesian approaches (and not solely ABC). At this point, Sonia Petrone, editor of Statistical Science, suggested we had a special issue on the whole issue of trends of interest and promise for Bayesian computational statistics. Joining forces, after some delays and failures to convince others to engage, or to produce multilevel papers with distinct vignettes, we eventually put together an additional four papers, where lead authors gathered further authors to produce this diverse picture of some incoming advances in the field. We have deliberated avoided topics which have excellent recent reviews— such as Stein’s method, sequential Monte Carlo, piecewise deterministic Markov processes— and topics which are still in their infancy, such as the relationship of Bayesian approaches to large language models (LLMs) and foundation models.
Within this issue, Past, Present, and Future of Software for Bayesian Inference from Erik Štrumbelj & al covers the state of the art in the most popular Bayesian software, reminding us of the massive impact BUGS has had on the adoption of Bayesian tools since its early introduction in the early 1990s (which I remember discovering at the Fourth Valencia meeting on Bayesian statistics in April 1991). With an interesting distinction between first and second generations, and a light foray of the potential third generation, maybe missing the role of LLMs in coding that are already impacting the approach to computing and the less immediate revolution brought by quantum computing. Winter & al.’s The Future of Bayesian Computation [TITLE TO CHANCE] is making a link with machine learning techniques, without looking at the scariest issue of how Bayesian inference can survive in a machine learning world! While it produces an additional foray into the blurry division between proper sampling (à la MCMC) and approximations, additional to the historical Martin et al. (2024), it articulates these aspects within a (deep) machine learning perspective, emphasizing the role of summaries produced by generative models exploiting the power of neural network computation/optimization. And the pivotal reliance on variational Bayes, which is the most active common denominator with machine learning. With further entries on major issues like distributed computing, opening on the important aspect of data protection and guaranteed privacy. We particularly like the clinical presentation of this paper with attention to automation and limitations. Normalizing flows actually link this paper with Heng, Bortoli and Doucet’s coverage of the Schrödinger bridge, which is a more focussed coverage of recent advances on possibly the next generation of posterior samplers. The final paper, Bayesian experimental design by Rainforth & al., provides a most convincing application of the methods exposed in the earlier papers in that the field of Bayesian design has hugely benefited from the occurrence of such tools to become a prevalent way of designing statistical experiments in real settings.
We feel the future of Bayesian computing is bright! The Monte Carlo revolution of the 1990s continues to be a huge influence on today’s work, and now is complemented by an exciting range of new directions informed by modern machine learning.
Dennis Prangle and Christian P Robert
Nature this week contains a prominent paper by Arute et al. reporting an experiment on a quantum computer running a simulation on a state-space of dimension 253 (which is the number of qubits in their machine, plus one dedicated to error correction if I get it right). With a million simulation of the computer state requiring 200 seconds. Which they claim would take 10,000 years (3 10¹¹ seconds) to run on a classical super-computer. And which could be used towards producing certified random numbers, an impressive claim given the intrinsic issue of qubit errors. (This part is not developed in the paper but I wonder how a random generator could handle such errors.)
“…a “challenger” generates a random quantum circuit C (i.e., a random sequence of 1-qubit and nearest-neighbor 2-qubit gates, of depth perhaps 20, acting on a 2D grid of n = 50 to 60 qubits). The challenger then sends C to the quantum computer, and asks it apply C to the all-0 initial state, measure the result in the {0,1} basis, send back whatever n-bit string was observed, and repeat some thousands or millions of times. Finally, using its knowledge of C, the classical challenger applies a statistical test to check whether the outputs are consistent with the QC having done this.” The blog of Scott Aaronson
I have tried reading the Nature paper but had trouble grasping the formidable nature of the simulation they were discussing, as it seems to be the reproduction by a simulation of a large quantum circuit of depth 20, as helpfully explained in the above quote. And checking the (non-uniform) distribution of the random simulation is the one expected. Which is the hard part and requires a classical (super-)computer to determine the theoretical distribution. And the News & Views entry in the same issue of Nature. According to Wikipedia, “the best known algorithm for simulating an arbitrary random quantum circuit requires an amount of time that scales exponentially with the number of qubits“. However, IBM (a competitor of Google in the quantum computer race) counter-claims that the simulation of the circuit takes only 2.5 days on a classical computer with optimised coding. (And this should be old news by the time this blog post comes out, since even a US candidate for the presidency has warned about it!)
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