control variates [seminar]

Today, Petros Dellaportas (whom I have know since the early days of MCMC, when we met in CIRM) gave a seminar at the Warwick algorithm seminar on control variates for MCMC, reminding me of his 2012 JRSS paper. Based on the Poisson equation and using a second control variate to stabilise the Monte Carlo approximation do the first control variate. The difference with usual control variates is finding a first approximate G(x)-q(y|x)G(Y) to F-πF. And the first Poisson equation is using α(x,y)q(y|x) rather than π. Then the second expands log α(x,y)q(y|x) to achieve a manageable term.

Abstract: We provide a general methodology to construct control variates for any discrete time random walk Metropolis and Metropolis-adjusted Langevin algorithm Markov chains that can achieve, in a post-processing manner and with a negligible additional computational cost, impressive variance reduction when compared to the standard MCMC ergodic averages. Our proposed estimators are based on an approximate solution of the Poisson equation for a multivariate Gaussian target densities of any dimension.

I wonder if there were a neural network version that would first build G from scratch and later optimise it towards solving the Poisson equation. As in this recent arXival I haven’t read (yet).

ISB@CIRM: through the looking glass

It’s now official!, thanks to the support of the Société Mathématique de France (SMF), the Centre National de la Recherche Scientifique (CNRS), and the Université Aix-Marseille, we are going to have a mirror workshop at CIRM, Marseille (France, not South Africa or Ohio!) gathering local Bayesians to attend ISBA 2021 together over the week of 28 June – 2 July, and share more than a virtual meeting room, while increasing the motivation to attend all sessions over a five day ultra-marathon! We also hope to have outdoor poster sessions around breaks.There is no registration fee and no support either, the only cost being the full-board on-site accommodation at CIRM to be paid upon arrival. Registration is open. Until we reach the upper limit set by the centre and depending on the dynamics of the pandemic (and of the administration). So feel free to apply if you are reasonably confident to be allowed and able to reach CIRM on the week of 28 June – 2 July. Which means travelling within the EU, at best.

CIRM in dire need of help

The International Mathematics Conference Centre, CIRM, located in Luminy, Marseille, France, has been deeply disrupted by the COVID-19 pandemic. Up to 60 % of the events planned there have been cancelled so far and all remaining conferences have gone virtual or at best hybrid, open to a remote audience, including in an interactive way. This has required important and unexpected investments. Furthermore, this crisis happened at the worst possible moment as CIRM had just finished doubling its infrastructure capacities. This is why I strongly support the call from the French Mathematical Society (SMF) to make a donation to CIRM before the end of the year, especially from researchers who benefited from its hospitality and unique environment.

Hélène Massam (1949-2020)

I was much saddened to hear yesterday that our friend and fellow Bayesian Hélène Massam passed away on August 22, 2020, following a cerebrovascular accident. She was professor of Statistics at York University, in Toronto, and, as her field of excellence covered [the geometry of] exponential families, Wishart distributions and graphical models, we met many times at both Bayesian and non-Bayesian conferences  (the first time may have been an IMS in Banff, years before BIRS was created). And always had enjoyable conversations on these occasions (in French since she was born in Marseille and only moved to Canada for her graduate studies in optimisation). Beyond her fundamental contributions to exponential families, especially Wishart distributions under different constraints [including the still opened 2007 Letac-Massam conjecture], and graphical models, where she produced conjugate priors for DAGs of all sorts, she served the community in many respects, including in the initial editorial board of Bayesian Analysis. I can also personally testify of her dedication as a referee as she helped with many papers along the years. She was also a wonderful person, with a great sense of humor and a love for hiking and mountains. Her demise is a true loss for the entire community and I can only wish her to keep hiking on new planes and cones in a different dimension. [Last month, Christian Genest (McGill University) and Xin Gao (York University) wrote a moving obituary including a complete biography of Hélène for the Statistical Society of Canada.]

QMC at CIRM