Archive for Bayes factors

ISBA 2021 grand finale

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on July 3, 2021 by xi'an

Last day of ISBA (and ISB@CIRM), or maybe half-day, since there are only five groups of sessions we can attend in Mediterranean time.

My first session was one on priors for mixtures, with 162⁺ attendees at 5:15am! (well, at 11:15 Wien or Marseille time), Gertrud Malsiner-Walli distinguishing between priors on number of components [in the model] vs number of clusters [in the data], with a minor question of mine whether or not a “prior” is appropriate for a data-dependent quantity. And Deborah Dunkel presenting [very early in the US!] anchor models for fighting label switching, which reminded me of the talk she gave at the mixture session of JSM 2018 in Vancouver. (With extensions to consistency and mixtures of regression.) And Clara Grazian debating on objective priors for the number of components in a mixture [in the Sydney evening], using loss functions to build these. Overall it seems there were many talks on mixtures and clustering this year.

After the lunch break, when several ISB@CIRM were about to leave, we ran the Objective Bayes contributed session, which actually included several Stein-like minimaxity talks. Plus one by Théo Moins from the patio of CIRM, with ciccadas in the background. Incredibly chaired by my friend Gonzalo, who had a question at the ready for each and every speaker! And then the Savage Awards II session. Which ceremony is postponed till Montréal next year. And which nominees are uniformly impressive!!! The winner will only be announced in September, via the ISBA Bulletin. Missing the ISBA general assembly for a dinner in Cassis. And being back for the Bayesian optimisation session.

I would have expected more talks at the boundary of BS & ML (as well as COVID and epidemic decision making), the dearth of which should be a cause for concern if researchers at this boundary do not prioritise ISBA meetings over more generic meetings like NeurIPS… (An exception was George Papamakarios’ talk on variational autoencoders in the Savage Awards II session.)

Many many thanks to the group of students at UConn involved in setting most of the Whova site and running the support throughout the conference. It indeed went on very smoothly and provided a worthwhile substitute for the 100% on-site version. Actually, I both hope for the COVID pandemic (or at least the restrictions attached to it) to abate and for the hybrid structure of meetings to stay, along with the multiplication of mirror workshops. Being together is essential to the DNA of conferences, but travelling to a single location is not so desirable, for many reasons. Looking for ISBA 2022, a year from now, either in Montréal, Québec, or in one of the mirror sites!

ISBA 2021 low key

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , , , , , , , , , on July 2, 2021 by xi'an

Fourth day of ISBA (and ISB@CIRM), which was a bit low key for me as I had a longer hike with my wife in the morning, including a swim in a sea as cold as the Annecy lake last month!, but nonetheless enjoyable and crystal clear, then attacked my pile of Biometrika submissions that had accumulated beyond the reasonable since last week, chased late participants who hadn’t paid yet, reviewed a paper that was due two weeks ago, chatted with participants before they left, discussed a research problem, and as a result ended attending only four sessions over the whole day. Including one about Models and Methods for Networks and Graphs, with interesting computation challenges, esp. in block models, the session in memoriam of Hélène Massam, where Gérard Letac (part of ISB@CIRM!), Jacek Wesolowski, and Reza Mohammadi, all coauthors of Hélène, made presentations on their joint advances. Hélène was born in Marseille, actually, in 1949, and even though she did not stay in France after her École Normale studies, it was a further commemoration to attend this session in her birth-place. I also found out about them working on the approximation of a ratio of normalising constants for the G-Wishart. The last session of my data was the Susie Bayarri memorial lecture, with Tamara Roderick as the lecturer. Reporting on an impressive bunch of tricks to reduce computing costs for hierarchical models with Gaussian processes.

ISBA 2021.3

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on July 1, 2021 by xi'an

Now on the third day which again started early with a 100% local j-ISBA session. (After a group run to and around Mont Puget, my first real run since 2020!!!) With a second round of talks by junior researchers from master to postdoc level. Again well-attended. A talk about Bayesian non-parametric sequential taxinomy by Alessandro Zito used the BayesANT acronym, which reminded me of the new vave group Adam and the Ants I was listening to forty years ago, in case they need a song as well as a logo! (Note that BayesANT is also used for a robot using Bayesian optimisation!) And more generally a wide variety in the themes. Thanks to the j-organisers of this 100% live session!

The next session was on PDMPs, which I helped organise, with Manon Michel speaking from Marseille, exploiting the symmetry around the gradient, which is distribution-free! Then, remotely, Kengo Kamatani, speaking from Tokyo, who expanded the high-dimensional scaling limit to the Zig-Zag sampler, exhibiting an argument against small refreshment rates, and Murray Pollock, from Newcastle, who exposed quite clearly the working principles of the Restore algorithm, including why coupling from the past was available in this setting. A well-attended session despite the early hour (in the USA).

Another session of interest for me [which I attended by myself as everyone else was at lunch in CIRM!] was the contributed C16 on variational and scalable inference that included a talk on hierarchical Monte Carlo fusion (with my friends Gareth and Murray as co-authors), Darren’s call to adopt functional programming in order to save Bayesian computing from extinction, normalising flows for modularisation, and Dennis’ adversarial solutions for Bayesian design, avoiding the computation of the evidence.

Wes Johnson’s lecture was about stories with setting prior distributions based on experts’ opinions. Which reminded me of the short paper Kaniav Kamary and myself wrote about ten years ago, in response to a paper on the topic in the American Statistician. And could not understand the discrepancy between two Bayes factors based on Normal versus Cauchy priors, until I was told they were mistakenly used repeatedly.

Rushing out of dinner, I attended both the non-parametric session (live with Marta and Antonio!) and the high-dimension computational session on Bayesian model choice (mute!). A bit of a schizophrenic moment, but allowing to get a rough picture in both areas. At once. Including an adaptive MCMC scheme for selecting models by Jim Griffin. Which could be run directly over the model space. With my ever-going wondering at the meaning of neighbour models.

ISBA 20.2.21

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , on June 30, 2021 by xi'an

A second day which started earlier and more smoothly with a 100% local j-ISBA session. (Not counting the invigorating swim in Morgiou!) With talks by junior researchers from master to postdoc level, as this ISBA mirror meeting was primarily designed for them, so that they could all present their work, towards gaining more visibility for their research and facilitating more interactions with the participants. CIRM also insisted on this aspect of the workshop, which was well-attended.

I alas had to skip the poster session [and the joys of gather.town] despite skipping lunch [BND], due to organisational constraints. Then attended the Approximate Bayesian computation section, including one talk by Geoff Nicholls on confidence estimation for ABC, following upon the talk given by Kate last evening. And one by Florian Maire on learning the bound in accept-reject algorithms on the go, as in Caffo et al. (2002), which I found quite exciting and opening new possibilities, esp. if the Markov chain thus produced can be recycled towards unbiasedness without getting the constant right! For instance, by Rao-Blackwellisation, multiple mixtures, black box importance sampling, whatever. (This also reminded me of the earlier Goffinet et al. 1996.)

Followed by another Bayesian (modeling and) computation session. With my old friend Peter Müller talking about mixture inference with dependent priors (and a saturated colour scheme!), Matteo Ruggieri [who could not make it to CIRM!] on computable Bayesian inference for HMMs. Providing an impressive improvement upon particle filters for approximating the evidence. Also bringing the most realistic Chinese restaurant with conveyor belt! And Ming Yuan Zhou using optimal transport to define distance between distributions. With two different conditional distributions depending on which marginal is first fixed. And a connection with GANs (of course!).

And it was great to watch and listen to my friend Alicia Carriquiry talking on forensic statistics and the case for (or not?!) Bayes factors. And remembering Dennis Lindley. And my friend Jim Berger on frequentism versus Bayes! Consistency seems innocuous as most Bayes procedures are. Empirical coverage is another kind of consistency, isn’t it?

A remark I made when re-typing the program for CIRM is that there are surprisingly few talks about COVID-19 overall, maybe due to the program being mostly set for ISBA 2020 in Kunming. Maybe because we are more cautious than the competition…?!

And, at last, despite a higher density of boars around the CIRM facilities, no one got hurt yesterday! Unless one counts the impact of the French defeat at the Euro 2021 on the football fans here…

false confidence, not fake news!

Posted in Books, Statistics with tags , , , , , on May 28, 2021 by xi'an

“…aerospace researchers have recognized a counterintuitive phenomenon in satellite conjunction analysis, known as probability dilution. That is, as uncertainty in the satellite trajectories increases, the epistemic probability of collision eventually decreases. Since trajectory uncertainty is driven by errors in the tracking data, the seemingly absurd implication of probability dilution is that lower quality data reduce the risk of collision.”

In 2019, Balch, Martin, and Ferson published a false confidence theorem [false confidence, not false theorem!] in the Proceedings of the Royal [astatistical] Society, motivated by satellite conjunction (i.e., fatal encounter) analysis. But discussing in fine the very meaning of a confidence statement. And returning to the century old opposition between randomness and epistemic uncertainty, aleatory versus epistemic probabilities.

“…the counterintuitiveness of probability dilution calls this [use of epistemic probability] into question, especially considering [its] unsettled status in the statistics and uncertainty quantification communities.”

The practical aspect of the paper is unclear in that the opposition of aleatory versus epistemic probabilities does not really apply when the model connecting the observables with the position of the satellites is unknown. And replaced with a stylised parametric model. When ignoring this aspect of uncertainty, the debate is mostly moot.

“…the problem with probability dilution is not the mathematics (…) if (…)  inappropriate, that inappropriateness must be rooted in a mismatch between the mathematics of probability theory and the epistemic uncertainty to which they are applied in conjunction analysis.”

The probability dilution phenomenon as described in the paper is that, when (posterior) uncertainty increases, the posterior probability of collision eventually decreases, which makes sense since poor precision implies the observed distance is less trustworthy and the satellite could be anywhere. To conclude that increasing the prior or epistemic uncertainty makes the satellites safer from collision is thus fairly absurd as it only concerns the confidence in the statement that there will be a collision. But I agree with the conclusion that the statement of a low posterior probability is a misleading risk metric because, just like p-values, it is a.s. taken at face value. Bayes factors do relativise this statement [but are not mentioned in the paper]. But with the spectre of Lindley-Jeffreys paradox looming in the background.

The authors’ notion of false confidence is formally a highly probable [in the sample space] report of a high belief in a subset A of the parameter set when the true parameter does not belong to A. Which holds for all epistemic probabilities in the sense that there always exists such a set A. A theorem that I see as related to the fact that integrating an epistemic probability statement [conditional on the data x] wrt the true sampling distribution [itself conditional on the parameter θ] is not coherent from a probabilistic standpoint. The resolution of the paradox follows a principle set by Ryan Martin and Chuanhai Liu, such that “it is almost a tautology that a statistical approach satisfying this criterion will not suffer from the severe false confidence phenomenon”, although it sounds to me that this is a weak patch on a highly perforated tyre, the erroneous interpretation of probabilistic statements as frequentist ones.