off to Edinburgh [and SMC 2024]

Today I am off to Edinburgh for the SMC 2024 workshop run by the ICMS. Looking forward meeting with long time friends and new ones, and learning about novel directions in the field. And returning to Edinburgh I last visited in 2019 for the opening of the Bayes Centre. Hoping to enjoy the nearby Arthur’s Seat volcano and maybe farther away Munroes, depending on the program, train schedules, and…weather forecasts!

sequential meetings in Edinburgh

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).

martingale posteriors

A new Royal Statistical Society Read Paper featuring Edwin Fong, Chris Holmes, and Steve Walker. Starting from the predictive

rather than from the posterior distribution on the parameter is a fairly novel idea, also pursued by Sonia Petrone and some of her coauthors. It thus adopts a de Finetti’s perspective while adding some substance to the rather metaphysical nature of the original. It however relies on the “existence” of an infinite sample in (1) that assumes a form of underlying model à la von Mises or at least an infinite population. The representation of a parameter θ as a function of an infinite sequence comes as a shock first but starts making sense when considering it as a functional of the underlying distribution. Of course, trading (modelling) a random “opaque” parameter θ for (envisioning) an infinite sequence of random (un)observations may sound like a sure loss rather than as a great deal, but it gives substance to the epistemic uncertainty about a distributional parameter, even when a model is assumed, as in Example 1, which defines θ in the usual parametric way (i.e., the mean of the iid variables). Furthermore, the link with bootstrap and even more Bayesian bootstrap becomes clear when θ is seen this way.

Always a fan of minimal loss approaches, but (2.4) defines either a moment or a true parameter value that depends on the parametric family indexed by θ. Hence does not exist outside the primary definition of said parametric family. The following construct of the empirical cdf based on the infinite sequence as providing the θ function is elegant but what is its Bayesian justification? (I did not read Appendix C.2. in full detail but could not spot the prior on F.)

“The resemblance of the martingale posterior to a bootstrap estimator should not have gone unnoticed”

I am always fan of minimal loss approaches, but I wonder at (2.4), as it defines either a moment or a true parameter value that depends on the parametric family indexed by θ. Hence it does not exist outside the primary definition of said parametric family, which limits its appeal. The following construct of the empirical cdf based on the infinite sequence as providing the θ function is elegant and connect with bootstrap, but I wonder at its Bayesian justification. (I did not read Appendix C.2. in full detail but could not spot a prior on F.)

While I completely missed the resemblance, it is indeed the case that, if the predictive at each step is build from the earlier “sample”, the support is not going to evolve. However, this is not particularly exciting as the Bayesian non-parametric estimator is most rudimentary. This seems to bring us back to Rubin (1981) ?! A Dirichlet prior is mentioned with no further detail. And I am getting confused at the complete lack of structure, prior, &tc. It seems to contradict the next section:

“While the prescription of (3.1) remains a subjective task, we find it to be no more subjective than the selection of a likelihood function”

Copulas!!! Again, I am very glad to see copulas involved in the analysis. However, I remain unclear as to why Corollary 1 implies that any sequence of copulas could do the job. Further, why does the Gaussian copula appear as the default choice? What is the computing cost of the update (4.4) after k steps? Similarly (4.7) is using a very special form of copula, with independent-across-dimension increments. I am also missing a guided tour on the implementation, as it sounds explosive in book-keeping and multiplying, while relying on a single hyperparameter in (4.5.2)?

In the illustration section, the use of the galaxy dataset may fail to appeal to Radford Neal, in a spirit similar to Chopin’s & Ridgway’s call to leave the Pima Indians alone, since he delivered a passionate lecture on the inappropriateness of a mixture model for this dataset (at ICMS in 2001). I am unclear as to where the number of modes is extracted from the infinite predictive. What is $\theta$ in this case?

Copulas!!! Although I am unclear why Corollary 1 implies that any sequence of copulas does the job. And why the Gaussian copula appears as the default choice. What is the computing cost of the update (4.4) after k steps? Similarly (4.7) is using a very special form of copula, with independent-across-dimension increments. Missing a guided tour on the implementation, as it sounds explosive in book-keeping and multiplying. A single hyperparameter (4.5.2)?

ICMS supports mirrors

Received an announcement from the International Centre for Mathematical Sciences (ICMS) in Edinburgh that they will support mirror meetings (albeit in the United Kindgom) as well as other inclusive initiatives:

• ICMS@: this programme allows organisers to hold ‘satellite events’, ICMS-funded activity at venues elsewhere in the UK with logistic support by the ICMS staff. The aim will be to enable more activities at a high level distributed throughout the country and to facilitate participation by those who cannot easily travel. There will be an additional emphasis on regions that have found it difficult to fund local events in the past.

• Funds to allow participants at ICMS workshops to extend their visits in the UK, especially for the purpose of visiting other institutions and engaging in extended research interaction.

• A visitor programme for researchers from low- and middle-income countries to come to the UK to attend workshops and fund their stay for up to three months.

• Workshops or schools for postgraduate students and early career researchers which can be of varying lengths and intensities.

• A fund to help people with caring responsibilities attend our events.

MCqMC 2022 in Linz, 17-22 July

At the end of MCqMC 2020, held on-line with the amazing support of ICMS in Edinburgh, the next location was announced as being Linz, Austria, hosted by the Johannes Kepler Universität I visited a few years ago (with a memorable run up a nearby hill!). Hopefully this will take place for real as well as on-line, but my prior is rather non-informed at the moment…