## Archive for University of Oxford

## congrats, Prof Rousseau!

Posted in Statistics with tags Advanced Grant, asymptotic Bayesian methods, department of statistics, ERC, EU, European Union, high dimensions, Judith Rousseau, University of Oxford on April 4, 2019 by xi'an## Bernoulli race particle filters

Posted in Books, pictures, Statistics, University life with tags auxiliary variable, Bernoulli distribution, Bernoulli factory, intractable constant, Jakob Bernoulli, Monte Carlo approximations, normalising constant, particle filters, University of Oxford on March 27, 2019 by xi'an**S**ebastian Schmon, Arnaud Doucet and George Deligiannidis have recently arXived an AISTATS paper with the above nice title. The motivation for the extension is facing intractable particle weights for state space models, as for instance in discretised diffusions. In most cases, actually, the weight associated with the optimal forward proposal involves an intractable integral which is the predictive of the current observed variate given the past hidden states. And in some cases, there exist unbiased and non-negative estimators of the targets, which can thus be substituted, *volens nolens*, to the original filter. As in many pseudo-marginal derivations, this new algorithm can be interpreted as targeting an augmented distribution that involves the auxiliary random variates behind the unbiased estimators of the particle weights. A worthwhile remark since it allows for the preservation of the original target as in (8) provided the auxiliary random variates are simulated from the right conditionals. (At least ideally as I have no clue when this is feasible.)

“if Bernoulli resampling is per-formed, the variance for any Monte Carlo estimate will be the same as if the true weights were known and one applies standard multinomial resampling.”

The Bernoulli race in the title stands for a version of the Bernoulli factory problem, where an intractable and bounded component of the weight can be turned into a probability, for which a Bernoulli draw is available, hence providing a Multinomial sampling with the intractable weights since replacing the exact probability with an estimate does not modify the Bernoulli distribution, amazingly so! Even with intractable normalising constants in particle filters. The practicality of the approach may however be restricted by the possibility of some intractable terms being very small and requiring many rejections for one acceptance, as the number of attempts is a compound geometric. The intractability may add to the time request the drawback of keeping this feature hidden as well. Or force some premature interruption in the settings of a parallel implementation.

## absint[he] post-doc on approximate Bayesian inference in Paris, Montpellier and Oxford

Posted in Statistics with tags ABC, Agence Nationale de la Recherche, ANR, approximate Bayesian inference, bois de Boulogne, La Défense, misspecified model, Paris, Paris-Saclay campus, PhD thesis, postdoctoral position, Université de Montpellier, Université Paris Dauphine, University of Oxford on March 18, 2019 by xi'anAs a consequence of its funding by the Agence Nationale de la Recherche (ANR) in 2018, the ABSint research conglomerate is now actively recruiting a post-doctoral collaborator for up to 24 months. The accronym ** ABSint** stands for Approximate Bayesian solutions for inference on large datasets and complex models. The ABSint conglomerate involves researchers located in Paris, Saclay, Montpelliers, as well as Lyon, Marseille, Nice. This call seeks candidates with an excellent research record and who are interested to collaborate with local researchers on approximate Bayesian techniques like ABC, variational Bayes, PAC-Bayes, Bayesian non-parametrics, scalable MCMC, and related topics. A potential direction of research would be the derivation of new Bayesian tools for model checking in such complex environments. The post-doctoral collaborator will be primarily located in Université Paris-Dauphine, with supported periods in Oxford and visits to Montpellier. No teaching duty is attached to this research position.

Applications can be submitted in either English or French. Sufficient working fluency in English is required. While mastering some French does help with daily life in France (!), it is not a prerequisite. The candidate must hold a PhD degree by the date of application (not the date of employment). Position opens on July 01, with possible accommodation for a later start in September or October.

Deadline for application is April 30 or until position filled. Estimated gross salary is around 2500 EUR, depending on experience (years) since PhD. Candidates should contact Christian Robert (gmail address: bayesianstatistics) with a detailed vita (CV) and a motivation letter including a research plan. Letters of recommendation may also be emailed to the same address.

## scalable Metropolis-Hastings

Posted in Books, Statistics, Travel with tags delayed acceptance, Fukui-Todo procedure, Hamiltonian Monte Carlo, Langevin MCMC algorithm, PDMP, scalable MCMC, scaling, Taylor expansion, thinning, University of Oxford on February 12, 2019 by xi'an**A**mong the flury of arXived papers of last week (414!), including a fair chunk of papers submitted to ICML 2019, I spotted one entry by Cornish et al. on scalable Metropolis-Hastings, which Arnaud Doucet had mentioned to me yesterday when in Oxford. The paper builds on the delayed acceptance paper we wrote with Marco Banterlé, Clara Grazian and Anthony Lee, itself relying on a factorisation decomposition of the likelihood, combined with control variate accelerating techniques. The factorisation of both the target and the proposal allows for a (less efficient) Metropolis-Hastings acceptance ratio that is the product

of individual Metropolis-Hastings acceptance ratios, but which allows for quicker rejection if one of the probabilities in the product is small, because the corresponding Bernoulli draw is zero with high probability. One advance made in Michel et al. (2017) [which I doubly missed] is that subsampling is achievable by thinning (as in PDMPs, where these authors have been quite active) through an algorithm of Shantikumar (1985) [described in Devroye’s bible]. Provided each Metropolis-Hastings probability can be lower bounded:

by a term where the transition *φ* does not depend on the index *i* in the product. The computing cost of the thinning process thus depends on the efficiency of the subsampling, namely whether or not the (Poisson) number of terms is much smaller than m, number of terms in the product. A neat trick in the current paper that extends the the Fukui-Todo procedure is to switch to the original Metropolis-Hastings when the overall lower bound is too small, recovering the geometric ergodicity of this original if it holds (**Theorem 2.1**). Another neat remark is that when using the naïve factorisation as the product of the n individual likelihoods, the resulting algorithm is sort of doomed as n grows, even with an optimal scaling of the proposals. To achieve scalability, the authors introduce a Taylor (i.e., Gaussian) approximation to each local target in the product and start the acceptance decomposition by using the resulting overall Gaussian approximation. Meaning that the remaining product is now made of ratios of targets over their local Taylor approximations, hence most likely close to one. And potentially lower-bounded by the remainder term in the Taylor expansion. Leading to the conclusion that, when everything goes well, meaning that the Taylor expansions can be conducted and the bounds derived for the appropriate expansion, the order of the Poisson scale is O(1/√n)..! The proposal for the Metropolis-Hastings move is actually tuned to the Gaussian approximation, appearing as a variant of the Langevin move or more exactly a discretization of an Hamiltonian move. Obviously, I cannot judge of the complexity in implementing this new scheme from just reading the paper, but this development on the split target is definitely an exciting prospect for handling huge datasets and their friends!

## Jeffreys priors for hypothesis testing [Bayesian reads #2]

Posted in Books, Statistics, University life with tags Arnold Zellner, Bayes factor, Bayesian tests of hypotheses, CDT, class, classics, Gaussian mixture, improper priors, Jeffreys prior, JRSSB, Kullback-Leibler divergence, Oxford, PhD course, Saint Giles cemetery, Susie Bayarri, Theory of Probability, University of Oxford on February 9, 2019 by xi'anA second (re)visit to a reference paper I gave to my OxWaSP students for the last round of this CDT joint program. Indeed, this may be my first complete read of Susie Bayarri and Gonzalo Garcia-Donato 2008 Series B paper, inspired by Jeffreys’, Zellner’s and Siow’s proposals in the Normal case. *(Disclaimer: I was not the JRSS B editor for this paper.) *Which I saw as a talk at the O’Bayes 2009 meeting in Phillie.

The paper aims at constructing formal rules for objective proper priors in testing embedded hypotheses, in the spirit of Jeffreys’ Theory of Probability “hidden gem” (Chapter 3). The proposal is based on symmetrised versions of the Kullback-Leibler divergence κ between null and alternative used in a transform like an inverse power of 1+κ. With a power large enough to make the prior proper. Eventually multiplied by a reference measure (i.e., the arbitrary choice of a dominating measure.) Can be generalised to any intrinsic loss (not to be confused with an intrinsic prior à la Berger and Pericchi!). Approximately Cauchy or Student’s t by a Taylor expansion. To be compared with Jeffreys’ original prior equal to the derivative of the atan transform of the root divergence (!). A delicate calibration by an effective sample size, lacking a general definition.

At the start the authors rightly insist on having the nuisance parameter v to differ for each model but… as we all often do they relapse back to having the “same ν” in both models for integrability reasons. Nuisance parameters make the definition of the divergence prior somewhat harder. Or somewhat arbitrary. Indeed, as in reference prior settings, the authors work first conditional on the nuisance then use a prior on ν that may be improper by the “same” argument. (Although *conditioning* is not the proper term if the marginal prior on ν is improper.)

The paper also contains an interesting case of the translated Exponential, where the prior is L¹ Student’s t with 2 degrees of freedom. And another one of mixture models albeit in the simple case of a location parameter on one component only.

## warm stone & cold morning light [jatp]

Posted in pictures, Travel, University life with tags England, jatp, Jesus College, neo-gothic architecture, Oxford colleges, OxWaSP, University of Oxford on January 30, 2019 by xi'an## BNP12

Posted in pictures, Statistics, Travel, University life with tags Bayesian nonparametrics, BNP12, Coventry, England, ISBA, Midlands, O'Bayes 2019, objective Bayes, Oxford, support, UK, University of Oxford, University of Warwick on October 9, 2018 by xi'an**T**he next BNP (Bayesian nonparametric) conference is taking place in Oxford (UK), prior to the O’Bayes 2019 conference in Warwick, in June 24-28 and June 29-July 2, respectively. At this stage, the Scientific Committee of BNP12 invites submissions for possible contributed talks. The deadline for submitting a title/abstract is 15th December 2018. And the submission of applications for travel support closes on 15th December 2018. Currently, there are 35 awards that could be either travel awards or accommodation awards. The support is for junior researchers (students currently enrolled in a Dphil (PhD) programme or having graduated after 1st October 2015). The applicant agrees to present her/his work at the conference as a poster or oraly if awarded the travel support.

As for O’Bayes 2019, we are currently composing the programme, following the 20 years tradition of these O’Bayes meetings of having the Scientific Committee (Marilena Barbieri, Ed George, Brunero Liseo, Luis Pericchi, Judith Rousseau and myself) inviting about 25 speakers to present their recent work and 25 discussants to… discuss these works. With a first day of introductory tutorials to Bayes, O’Bayes and beyond. I (successfully) proposed this date and location to the O’Bayes board to take advantage of the nonparametric Bayes community present in the vicinity so that they could attend both meetings at limited cost and carbon impact.