stratified MCMC

When working last week with a student, we came across [the slides of a talk at ICERM by Brian van Koten about] a stratified MCMC method whose core idea is to solve a eigenvector equation z’=z’F associated with the masses of “partition” functions Ψ evaluated at the target. (The arXived paper is also available since 2017 but I did not check it in more details.)Although the “partition” functions need to overlap for the matrix not to be diagonal (actually the only case that does not work is when these functions are truly indicator functions). As in other forms of stratified sampling, the practical difficulty is in picking the functions Ψ so that the evaluation of the terms of the matrix F is not overly impacted by the Monte Carlo error. If spending too much time in estimating these terms, there is not a clear gain in switching to stratified sampling, which may be why it is not particularly developed in the MCMC literature….

As an interesting aside, the illustration in this talk comes from the Mexican stamp thickness data I also used in my earlier mixture papers, concerning the 1872 Hidalgo issue that was printed on different qualities of paper. This makes the number k of components somewhat uncertain, although k=3 is sometimes used as a default. Hence a parameter and simulation space of dimension 8, even though the method is used toward approximating the marginal posteriors on the weights λ¹ and λ².

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.]

marginal likelihood with large amounts of missing data

In 2018, Panayiota Touloupou, research fellow at Warwick, and her co-authors published a paper in Bayesian analysis that somehow escaped my radar, despite standing in my first circle of topics of interest! They construct an importance sampling approach to the approximation of the marginal likelihood, the importance function being approximated from a preliminary MCMC run, and consider the special case when the sampling density (i.e., the likelihood) can be represented as the marginal of a joint density. While this demarginalisation perspective is rather usual, the central point they make is that it is more efficient to estimate the sampling density based on the auxiliary or latent variables than to consider the joint posterior distribution of parameter and latent in the importance sampler. This induces a considerable reduction in dimension and hence explains (in part) why the approach should prove more efficient. Even though the approximation itself is costly, at about 5 seconds per marginal likelihood. But a nice feature of the paper is to include the above graph that includes both computing time and variability for different methods (the blue range corresponding to the marginal importance solution, the red range to RJMCMC and the green range to Chib’s estimate). Note that bridge sampling does not appear on the picture but returns a variability that is similar to the proposed methodology.

JB³ [Junior Bayes beyond the borders]

Bocconi and j-ISBA are launcing a webinar series for and by junior Bayesian researchers. The first talk is on 25 June, 25 at 3pm UTC/GMT (5pm CET) with Francois-Xavier Briol, one of the laureates of the 2020 Savage Thesis Prize (and a former graduate of OxWaSP, the Oxford-Warwick doctoral training program), on Stein’s method for Bayesian computation, with as a discussant Nicolas Chopin.

As pointed out on their webpage,

Due to the importance of the above endeavor, JB³ will continue after the health emergency as an annual series. It will include various refinements aimed at increasing the involvement of the whole junior Bayesian community and facilitating a broader participation to the online seminars all over the world via various online solutions.

Thanks to all my friends at Bocconi for running this experiment!

data science [down] under the hood [webinar]