## integral theorems for Monte Carlo

Posted in Books, pictures, Statistics with tags , , , , , , , on August 12, 2021 by xi'an

Nhat Ho and Stephen G. Walker have just arXived a paper on the use of (Fourier) integral theorems for Monte Carlo estimators, following the earlier entry of Parzen: namely that for any integrable function,

$m(y)=\frac{1}{(2\pi)^d}\int_{\mathbb R^d}\int_{\mathbb R^d}\cos(s^\text{T}(y-x))m(x)\text dx\text ds$

which can be turned into an estimator of a density m based on a sample from m. This identity can be rewritten as

$m(y)=\lim_{R\to\infty}\frac{1}{\pi^d}\int_{\mathbb R^d}\prod_{i=1}^d\dfrac{\sin(R(y_i-x_i))}{y_i-x_i}\;m(x)\,\text dx$

and the paper generalises this identity to all cyclic functions. Even though it establishes that sin is the optimal choice. After reading this neat result, I however remain uncertain on how this could help with Monte Carlo integration.

## post-COVID post-conference mood

Posted in Kids, Running, Travel, University life with tags , , , , , , , , , , , , , on August 27, 2020 by xi'an

Nature ran a 4-page comment on the post-COVID future of massive conferences (NeurIPS or JSM style) and on how to make them less carbon greedy. Some of their common-sense suggestions come close to what I had suggested a while ago and some became promptly implemented in these times of COVID-19 travel restrictions, as, e.g., to systematically include virtual attendance option(s), with provisions from one’s institutions for quality time (as if one was indeed away), to add multiple (3?) regional hubs to a single location, which also offers the perk of a round-the-clock meeting, with an optimisation of the three places chosen to minimise (estimated) total flight distances for the potential participants, as in e.g. choosing U.S. central Chicago rather than extremes like Seattle or Miami, and possibly adding Tokyo and Paris, to reduce the frequency of the monster meetings by coordinating with sister societies, to enforce an individual or institutional maximum yearly budget, to have corporate sponsors turning from travel support to improving remote access in less favoured countries.

Obviously, it seems difficult to completely switch to a fully virtual solution, as attending a conference has many academic dimensions to be accounted for, but the “big ones” should be the first to shrink, if only because the most impacting. And also because small, high quality workshops have much more impact research-wise on their attendants. With the above still offering some savings. And also the possibility to bypass financial, personal, visa, political, life-threatening impossibilities to attend a meeting in a specific foreign country. Provided uncensored remote communication tools are allowed or possible from the said  country. (Calling for the question, barring financial difficulties, and once COVID-related restrictions have been lifted, what are the countries where everyone could consider attending?!)

This year, before lockdown forced the cancellation of ABC in Grenoble, we had set a mirror version in Warwick. Which led us to create the One World ABC seminar. The Bernoulli-IMS World congress was postponed by one year but a few dedicated volunteers managed to build within a few weeks a free impressive virtual substitute with more than 600 talks and close to 2000 participants (so far). Remember it is to take place on 24-28 August, on different time zones and with ten live plenaries repeated twice to this effect.

Next year, we still hope to organise an Objective Bayesian workshop at Casa Matemática Oaxaca (CMO) in México and the current sanitary conditions imply a reduction of the physically present participants by two thirds. Meaning for certain a remote component and possibly a mirror location depending on the state of the World in December 2021.

## U of T sunset [jatp]

Posted in pictures, Running, Travel, University life with tags , , , , , on December 14, 2017 by xi'an

## Au’Bayes 17

Posted in Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , on December 14, 2017 by xi'an

Some notes scribbled during the O’Bayes 17 conference in Austin, not reflecting on the highly diverse range of talks. And many new faces and topics, meaning O’Bayes is alive and evolving. With all possible objectivity, a fantastic conference! (Not even mentioning the bars where Peter Müller hosted the poster sessions, a feat I would have loved to see duplicated for the posters of ISBA 2018… Or the Ethiopian restaurant just around the corner with the right amount of fierce spices!)

The wiki on objective, reference, vague, neutral [or whichever label one favours] priors that was suggested at the previous O’Bayes meeting in Valencià, was introduced as Wikiprevia by Gonzalo Garcia-Donato. It aims at classifying recommended priors in most of the classical models, along with discussion panels, and it should soon get an official launch, when contributors will be welcome to include articles in a wiki principle. I wish the best to this venture which, I hope, will induce O’Bayesians to contribute actively.

In a brilliant talk that quickly reverted my jetlag doziness, Peter Grünwald returned to the topic he presented last year in Sardinia, namely safe Bayes or powered-down likelihoods to handle some degree of misspecification, with a further twist of introducing an impossible value `o’ that captures missing mass (to be called Peter’s demon?!), which absolute necessity I did not perceive. Food for thoughts, definitely. (But I feel that the only safe Bayes is the dead Bayes, as protecting against all kinds of mispecifications means no action is possible.)

I also appreciated Cristiano Villa’s approach to constructing prior weights in model comparison from a principled and decision-theoretic perspective even though I felt that the notion of ranking parameter importance required too much input to be practically feasible. (Unless I missed that point.)

Laura Ventura gave her talk on using for ABC various scores or estimating equations as summary statistics, rather than the corresponding M-estimators, which offers the appealing feature of reducing computation while being asymptotically equivalent. (A feature we also exploited for the regular score function in our ABC paper with Gael, David, Brendan, and Wonapree.) She mentioned the Hyvärinen score [of which I first heard in Padova!] as a way to bypass issues related to doubly intractable likelihoods. Which is a most interesting proposal that bypasses (ABC) simulations from such complex targets by exploiting a pseudo-posterior.

Veronika Rockova presented a recent work on concentration rates for regression tree methods that produce a rigorous analysis of these methods. Showing that the spike & slab priors plus BART [equals spike & tree] achieve sparsity and optimal concentration. In an oracle sense. With a side entry on assembling partition trees towards creating a new form of BART. Which made me wonder whether or not this was also applicable to random forests. Although they are not exactly Bayes. Demanding work in terms of the theory behind but with impressive consequences!

Just before I left O’Bayes 17 for Houston airport, Nick Polson, along with Peter McCullach, proposed an intriguing notion of sparse Bayes factors, which corresponds to the limit of a Bayes factor when the prior probability υ of the null goes to zero. When the limiting prior is replaced with an exceedance measure that can be normalised into a distribution, but does it make the limit a special prior? Linking  υ with the prior under the null is not an issue (this was the basis of my 1992 Lindley paradox paper) but the sequence of priors indexed by υ need be chosen. And reading from the paper at Houston airport, I could not spot a construction principle that would lead to a reference prior of sorts. One thing that Nick mentioned during his talk was that we observed directly realisations of the data marginal, but this is generally not the case as the observations are associated with a given value of the parameter, not one for each observation.The next edition of the O’Bayes conference will be in… Warwick on June 29-July 2, as I volunteered to organise this edition (16 years after O’Bayes 03 in Aussois!) just after the BNP meeting in Oxford on June 23-28, hopefully creating the environment for fruitful interactions between both communities! (And jumping from Au’Bayes to Wa’Bayes.)

## O’Bayes 2017 group photograph

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , on December 13, 2017 by xi'an