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sequential meetings in Edinburgh

Posted in Books, Kids, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , on October 24, 2023 by xi'an


There will be not one but two consecutive events in Edinburgh next May²⁴ on sequential Monte Carlo methods! Both hosted by the fantastic International Centre for Mathematical Sciences (ICMS) in Edinburgh Olde Town. Within the Bayes Centre. And running distance to Arthur’s Seat. (Reminding me of my first ICMS workshop in 2001 run with Mike Titterington. May have been my first week long visit to Edinburgh as well…)

First, a Summer School on Bayesian filtering: fundamental theory and numerical methods (SSBF 2024), Edinburgh (UK), May 6-10, 2024. This summer (in the Scottish sense!) school will cover topics related to fundamental theory, state-of-the-art methodologies, and real-world applications.

Second, a Sequential Monte Carlo workshop (SMC 2024), the week later, on May 13-17, 2024. The workshop will cover topics related to sequential Monte Carlo and nearby fields, from theory to applications, following earlier workshops in the series. Including the one at CREST in 2015.

Thanks to Víctor Elvira, Jana de Wiljes, and Dan Crisan for this double deal (and the opportunity to return to Scotland for the first time since the pandemic).

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to be demolished!

Posted in Books, pictures, University life with tags , , , , , , , , , on May 8, 2022 by xi'an

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SMC 22 coming soon!

Posted in Statistics with tags , , , , , , , , , on February 7, 2022 by xi'an

The 5th Workshop on Sequential Monte Carlo Methods (SMC 2022) will take place in Madrid on 4-6 May 2022. More precisely on the Leganés campus of Universidad Carlos III de Madrid. Registrations are now open, with very modest registration fees and the list of invited speakers is available on the webpage of the workshop. (The SMC 2020 workshop was cancelled due to the COVID-19 pandemic. An earlier workshop took place at CREST in 2015.)

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David Cox (1924-2022)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , on January 20, 2022 by xi'an

It is with much sadness that I heard from Oxford yesterday night that David Cox had passed away. Hither goes a giant of the field, whose contributions to theoretical and methodological statistics are enormous and whose impact on society is truly exceptional. He was the first recipient of the International Prize in Statistics in 2016 (aka the “Nobel of Statistics”) among many awards and a Fellow of the Royal Society among many other recognitions. He was also the editor of Biometrika for 25 years (!) and was still submitting papers to the journal a few month ago. Statistical Science published a conversation between Nancy Reid and him that tells a lot about the man and his amazing modesty. While I had met him in 1989, when he was visiting Cornell University as a distinguished visitor (and when I drove him to the house of Anne and George Casella for dinner once), then again in the 1990s when he came on a two-day visit to CREST,  we only really had a significant conversation in 2011 (!), when David and I attended the colloquium in honour of Mike Titterington in Glasgow and he proved to be most interested in the ABC algorithm. He published a connected paper in Biometrika the year after, with Christiana Katsonaki. We met a few more times later, always in Oxford, to again discuss ABC. In each occasion, he was incredibly kind and considerate.

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distributed evidence

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , , , on December 16, 2021 by xi'an

Alexander Buchholz (who did his PhD at CREST with Nicolas Chopin), Daniel Ahfock, and my friend Sylvia Richardson published a great paper on the distributed computation of Bayesian evidence in Bayesian Analysis. The setting is one of distributed data from several sources with no communication between them, which relates to consensus Monte Carlo even though model choice has not been particularly studied from that perspective. The authors operate under the assumption of conditionally conjugate models, i.e., the existence of a data augmentation scheme into an exponential family so that conjugate priors can be used. For a division of the data into S blocks, the fundamental identity in the paper is

p(y) = \alpha^S \prod_{s=1}^S \tilde p(y_s) \int \prod_{s=1}^S \tilde p(\theta|y_s)\,\text d\theta

where α is the normalising constant of the sub-prior exp{log[p(θ)]/S} and the other terms are associated with this prior. Under the conditionally conjugate assumption, the integral can be approximated based on the latent variables. Most interestingly, the associated variance is directly connected with the variance of

p(z_{1:S}|y)\Big/\prod_{s=1}^S \tilde p(z_s|y_s)

under the joint:

“The variance of the ratio measures the quality of the product of the conditional sub-posterior as an importance sample proposal distribution.”

Assuming this variance is finite (which is likely). An approximate alternative is proposed, namely to replace the exact sub-posterior with a Normal distribution, as in consensus Monte Carlo, which should obviously require some consideration as to which parameterisation of the model produces the “most normal” (or the least abnormal!) posterior. And ensures a finite variance in the importance sampling approximation (as ensured by the strong bounds in Proposition 5). A problem shared by the bridgesampling package.

“…if the error that comes from MCMC sampling is relatively small and that the shard sizes are large enough so that the quality of the subposterior normal approximation is reasonable, our suggested approach will result in good approximations of the full data set marginal likelihood.”

The resulting approximation can also be handy in conjunction with reversible jump MCMC, in the sense that RJMCMC algorithms can be run in parallel on different chunks or shards of the entire dataset. Although the computing gain may be reduced by the need for separate approximations.

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