invited sessions at BayesComp [submissions open]

The call for invited sessions at BayesComp 2022 is now open, submission can be done via Google Form. Submissions are due by August 7. If you have any questions, please email to bayescomp2023 on Gmail. And if you want to contribute to AG::DC, please email Anto, Heikki or me!

day five at ISBA 22

Woke up even earlier today! Which left me time to work on switching to Leonard Cohen’s song titles for my slide frametitles this afternoon (last talk of the whole conference!), run once again to Mon(t) Royal as all pools are closed (Happy Canada Day!, except to “freedom convoy” antivaxxxers.) Which led to me meeting a raccoon by the side of the path (and moroons feeding wildlife).

Had an exciting time at the morning session, where Giacomo Zanella (formerly Warwick) talked on a mixture approach to leave-one-out predictives, with pseudo-harmonic mean representation, averaging inverse density across all observations. Better than harmonic? Some assumptions allow for finite variance, although I am missing the deep argument (in part due to Giacomo’s machine-gun delivery pace!) Then Alicia Corbella (Warwick) presented a promising entry into PDMP by proposing an automated zig-zag sampler. Pointing out on the side to Joris Bierkens’ webpage on the state-of-the-art PDMP methodology. In this approach, joint with with my other Warwick colleagues Simon Spencer and Gareth Roberts, the zig-zag sampler relies on automatic differentiation and sub-sampling and bound derivation, with “no further information on the target needed”. And finaly Chris Carmona presented a joint work with Geoff Nicholls that is merging merging cut posteriors and variational inference to create a meta posterior. Work and talk were motivated by a nice medieval linguistic problem where the latent variables impact the (convergence of the) MCMC algorithm [as in our k-nearest neighbour experience]. Interestingly using normalising [neural spline] flows. The pseudo-posterior seems to depend very much on their modularization rate η, which penalises how much one module influences the next one.

In the aft, I attended sort of by chance [due to a missing speaker in the copula session] to the end of a session on migration modelling, with a talk by Jason Hilton and Martin Hinsch focussing on the 2015’s mass exodus of Syrians through the Mediterranean,  away from the joint evils of al-Hassad and ISIS. As this was a tragedy whose modelling I had vainly tried to contribute to, I was obviously captivated and frustrated (leaning of the IOM missing migrant project!) Fitting the agent-based model was actually using ABC, and most particularly our ABC-PMC!!!

My own and final session had Gareth (Warwick) presenting his recent work with Jun Yang and Kryzs Łatuszyński (Warwick) on the stereoscopic projection improvement over regular MCMC, which involves turning the target into a distribution supported by an hypersphere and hence considering a distribution with compact support and higher efficiency. Kryzs had explained the principle while driving back from Gregynog two months ago. The idea is somewhat similar to our origaMCMC, which I presented at MCqMC 2016 in Stanford (and never completed), except our projection was inside a ball. Looking forward the adaptive version, in the making!

And to conclude this subjective journal from the ISBA conference, borrowing this title by (Westmount born) Leonard Cohen, “Hey, that’s not a way to say goodbye”… To paraphrase Bilbo Baggins, I have not interacted with at least half the participants half as much as I would have liked. But this was still a reunion, albeit in the new Normal. Hopefully, the conference will not have induced a massive COVID cluster on top of numerous scientific and social exchanges! The following days will tell. Congrats to the ISBA 2022 organisers for achieving a most successful event in these times of uncertainty. And looking forward the 2024 next edition in Ca’Foscari, Venezia!!!

 

ACDC versus ABC

At the Bayes, Fiducial and Frequentist workshop last month, I discussed with the authors of this newly arXived paper, Approximate confidence distribution computing, Suzanne Thornton and Min-ge Xie. Which they abbreviate as ACC and not as ACDC. While I have discussed the notion of confidence distribution in some earlier posts, this paper aims at producing proper frequentist coverage within a likelihood-free setting. Given the proximity with our recent paper on the asymptotics of ABC, as well as with Li and Fearnhead (2016) parallel endeavour, it is difficult (for me) to spot the actual distinction between ACC and ABC given that we also achieve (asymptotically) proper coverage when the limiting ABC distribution is Gaussian, which is the case for a tolerance decreasing quickly enough to zero (in the sample size).

“Inference from the ABC posterior will always be difficult to justify within a Bayesian framework.”

Indeed the ACC setting is eerily similar to ABC apart from the potential of the generating distribution to be data dependent. (Which is fine when considering that the confidence distributions have no Bayesian motivation but are a tool to ensure proper frequentist coverage.) That it is “able to offer theoretical support for ABC” (p.5) is unclear to me, given both this data dependence and the constraints it imposes on the [sampling and algorithmic] setting. Similarly, I do not understand how the authors “are not committing the error of doubly using the data” (p.5) and why they should be concerned about it, standing outside the Bayesian framework. If the prior involves the data as in the Cauchy location example, it literally uses the data [once], followed by an ABC comparison between simulated and actual data, that uses the data [a second time].

“Rather than engaging in a pursuit to define a moving target such as [a range of posterior distributions], ACC maintains a consistently clear frequentist interpretation (…) and thereby offers a consistently cohesive interpretation of likelihood-free methods.”

The frequentist coverage guarantee comes from a bootstrap-like assumption that [with tolerance equal to zero] the distribution of the ABC/ACC/ACDC random parameter around an estimate of the parameter given the summary statistic is identical to the [frequentist] distribution of this estimate around the true parameter [given the true parameter, although this conditioning makes no sense outside a Bayesian framework]. (There must be a typo in the paper when the authors define [p.10] the estimator as minimising the derivative of the density of the summary statistic, while still calling it an MLE.) That this bootstrap-like assumption holds is established (in Theorem 1) under a CLT on this MLE and assumptions on the data-dependent proposal that connect it to the density of the summary statistic. Connection that seem to imply a data-dependence as well as a certain knowledge about this density. What I find most surprising in this derivation is the total absence of conditions or even discussion on the tolerance level which, as we have shown, is paramount to the validation or invalidation of ABC inference. It sounds like the authors of Approximate confidence distribution computing are setting ε equal to zero for those theoretical derivations. While in practice they apply rules [for choosing ε] they do not voice out, but which result in very different acceptance rates for the ACC version they oppose to an ABC version. (In all illustrations, it seems that ε=0.1, which does not make much sense.) All in all, I am thus rather skeptical about the practical implications of the paper in that it seems to achieve confidence guarantees by first assuming proper if implicit choices of summary statistics and parameter generating distribution.

three ½ [out of 159] versions of Johnny B. Goode