persuasive (and Oceanic) privacy

I am quite excited about the paper James Baillie, Joshua Bon, Judith Rousseau, and myself just arXived! A novel framework for measuring privacy we have been working on for at least the past year, partly through the previous Les Houches privacy workshops. In the spirit of these workshops and the larger scale ERC Synergy grant OCEAN, we develop therein a rather generic Bayesian game-theoretic perspective on achieving statistical privacy. It involves a Sender (observing the original data and delivering a limited output) and a Receiver (with potential adversarial intentions). The paper mostly focus on setting a theoretical framework, including the creation of new, purpose-driven privacy definitions that are rigorously justified, while also allowing for the assessment of existing privacy guarantees through game theory. While this was not our original intent, we show that pure and probabilistic differential privacy notions, in the Dwork et al. (2006) sense, are special cases of our framework. This setting provides new interpretations of the post-processing inequality. Furthermore, and somewhat more importantly, we also prove that our privacy guarantees can be established for deterministic algorithms, which are outside current privacy standards. Hopefully, we’ll make further progress at the incoming privacy workshop next month, to be held in Venice (again).

4th Bayesian Nonparametrics Networking Workshop [call for contributions]

Scottish June

I just found out that three almost consecutive events of academic interest are taking place in Scotland next Spring: first, our very own Approximately Bayes ICMS workshop (on the Isle of Skye, rather than at the Bayes Centre in Edinburgh, where we held ABC in Edinburgh), on 17-22 May

the SIAM Conference on Optimization (OP26) in Edinburgh on 2-5 June

and the Monte Carlo + quasi Monte Carlo (MCqMC 2026) conference in Edinburgh on 8-11 June

While I cannot realistically (!) attend all of these events, this accumulation of meetings is a perfect opportunity to enjoy the Athens of the North (aka Dùn Èideann, from which Dunnedin in New Zealand originates!). And the surrounding mountains.

Advances in MCMC Methods [10-12 Dec, EURANDOM]

on stopping rules

The workshop in Chennai and its focus on sequential procedures made me realise (among other things) I had never read Cornfield’s 1966 TAS paper on sequential testing and the likelihood principle:

“By sequential analysis I mean any form of analysis in which the conclusion depends not only on the data, but also on the stopping rule.”

Written with little maths and formalism, this paper argues that keeping a fixed critical level amounts to keeping a fixed amount of evidence. Hence constituting an early critique of p-values even though not expressed in such terms. The part of the paper related with the likelihood principle does not address testing or evidence in a Bayesian way. As a side (late awakening) remark, iid observations in sequential settings are not longer independent, conditional on the stopping rule realisation N=n, since they are constrained by the fact that the stopping rule realisation is n and not n-1, n-2, …  For a short while, I thought it was in turn impacting the distribution of any “sufficient” statistic one may propose, with a normalising constant that depends on the unknown parameter and hence cannot be neglected. Over all those years, I had never though of the modification of sufficiency characteristics in such contexts. But in fine the pair made of the value of the stopping rule and of the unsequential sufficient statistics proves enough. And the normalisation constant is the probability that the stopping rule.. stops!, which is equal to one! For the same short while, I was then wondering that the stopping rule principle!

“my second line of argument that there is a reasonable alternative explication of the idea of inference and one which leads to the rejection of sequential analysis. This explication is provided by the likelihood principle—which states that all observations leading to the same likelihood function should lead to the same conclusion.”

I thus went back to the fundamentals (!), namely [freely available] Bernardo’s and Smith’s Section 5.1.4 (reproduced in EJ’s Stopping rule appendix, also citing Cornfield at length), where the likelihood is properly defined by the joint density of the stopping rule τ and the attached sample at their realised values. And failing in the end (and a discussion with Judith)nto spot a missing normalisation constant.