**R**ecently, I have been contacted by a mainstream statistics journal to write a review of Rao-Blackwellisation techniques in computational statistics, in connection with an issue celebrating C.R. Rao’s 100th birthday. As many many techniques can be interpreted as weak forms of Rao-Blackwellisation, as e.g. all auxiliary variable approaches, I am clearly facing an abundance of riches and would thus welcome suggestions from Og’s readers on the major advances in Monte Carlo methods that can be connected with the Rao-Blackwell-Kolmogorov theorem. (On the personal and anecdotal side, I only met C.R. Rao once, in 1988, when he came for a seminar at Purdue University where I was spending the year.)

## Archive for computational statistics

## Rao-Blackwellisation, a review in the making

Posted in Statistics with tags Andrei Kolmogorov, birthday, C.R. Rao, computational statistics, David Blackwell, Monte Carlo methods, Purdue University, Rao-Blackwell theorem, Rao-Blackwellisation, review, survey on March 17, 2020 by xi'an## MCMC, with common misunderstandings

Posted in Books, pictures, R, Statistics, University life with tags ABC, Bayesian computing, computational statistics, Gibbs sampling, Handbook of Computational Statistics and Data Science, HMC, IMS Lawrence D. Brown PhD Student Award, MCMC, PhD thesis, Q&A format, Statistics and Computing, survey, variational Bayes methods on January 27, 2020 by xi'an**A**s I was asked to write a chapter on MCMC methods for an incoming *Handbook of Computational Statistics and Data Science*, published by Wiley, rather than cautiously declining!, I decided to recycle the answers I wrote on X validated to what I considered to be the most characteristic misunderstandings about MCMC and other computing methods, using as background the introduction produced by Wu Changye in his PhD thesis. Waiting for the opinion of the editors of the *Handbook* on this Q&A style. The outcome is certainly lighter than other recent surveys like the one we wrote with Peter Green, Krys Latuszinski, and Marcelo Pereyra, for Statistics and Computing, or the one with Victor Elvira, Nick Tawn, and Changye Wu.

## probabilistic methods in computational statistics [workshop]

Posted in pictures, Statistics, Travel, University life with tags Évry, computational statistics, France, INT, partly observed Markov models, probabilistic numerics, Randal Douc, RER C, Télecom Sudparis, workshop on November 5, 2019 by xi'an**A** one-day workshop is organised at Telecom Sudparis, Évry, on 22 November by R. Douc, F. Portier and F. Roueff. On the “hot topics” concerned with probabilistic methods in computational statistics. The workshop is funded by the project “Big-Pomm”, which strengthens the links between LTCI (Telecom Paristech) and SAMOVAR (Telecom Sudparis) around research projects implying partially observed Markov models. The participation to the workshop is free but registration is required for having access to the lunch buffet (40 participants max). (Évry is located 20km south of Paris, with trains on the RER C line.)

## PhD studenships at Warwick

Posted in Kids, pictures, Statistics, University life with tags Brexit, CDT, Centre for Doctoral Training in Mathematics and Statistics, computational statistics, European Union, mathematical statistics, OxWaSP, PhD fellowship, University of Warwick on May 2, 2019 by xi'an

**T**here is an exciting opening for several PhD positions at Warwick, in the departments of Statistics and of Mathematics, as part of the Centre for Doctoral Training in Mathematics and Statistics newly created by the University. CDT studentships are funded for four years and funding is open to students from the European Union without restrictions. (No Brexit!) Funding includes a stipend at UK/RI rates and tuition fees at UK/EU rates. Applications are made via the University of Warwick Online Application Portal and should be made as quickly as possible since the funding will be allocated on a first come first serve basis. For more details, contact the CDT director, Martyn Plummer. I cannot but strongly encourage interested students to apply as this is a great opportunity to start a research career in a fantastic department!

## computational statistics and molecular simulation [18w5023]

Posted in pictures, Statistics, Travel, University life with tags 18w5023, Benzécri, BIRS, Casa Matemática Oaxaca, CMO, computational statistics, HMC, Jussieu, Mexico, molecular dynamics, Monte Carlos Statistical Methods, nested sampling, numerical integrator, path sampling, workshop on November 19, 2018 by xi'an**T**he last day of the X fertilisation workshop at the casa matematicà Oaxaca, there were only three talks and only half of the participants. I lost the subtleties of the first talk by Andrea Agazzi on large deviations for chemical reactions, due to an emergency at work (Warwick). The second talk by Igor Barahona was somewhat disconnected from the rest of the conference, working on document textual analysis by way of algebraic data analysis (analyse des données) methods à la Benzécri. (Who was my office neighbour at Jussieu in the early 1990s.) In the last and final talk, Eric Vanden-Eijden made a link between importance sampling and PDMP, as an integral can be expressed via a trajectory of a path. A generalisation of path sampling, for almost any ODE. But also a competitor to nested sampling, waiting for the path to reach an Hamiltonian level, without some of the difficulties plaguing nested sampling like resampling. And involving continuous time processes. (Is there a continuous time version of ABC as well?!) Returning unbiased estimators of mean (the original integral) and variance. Example of a mixture example in dimension d=10 with k=50 components using only 100 paths.

## computational statistics and molecular simulation [18w5023]

Posted in pictures, Statistics, Travel, University life with tags 18w5023, BIRS, Casa Matemática Oaxaca, CMO, computational statistics, HMC, hypocoercivity, Institut Henri Poincaré, Mexico, molecular dynamics, Monte Carlos Statistical Methods, overdamped Langevin algorithm, PDMP, workshop on November 16, 2018 by xi'an**T**his Thursday, our X fertilisation workshop at the interface between molecular dynamics and Monte Carlo statistical methods saw a wee bit of reduction in the audience as some participants had already left Oaxaca. Meaning they missed the talk of Christophe Andrieu on hypocoercivity which could have been another hand-on lecture, given the highly pedagogical contents of the talk. I had seen some parts of the talk in MCqMC 2018 in Rennes and at NUS, but still enjoyed the whole of it very much, and so did the audience given the induced discussion. For instance, previously, I had not seen the connection between the guided random walks of Gustafson and Diaconis, and continuous time processes like PDMP. Which Christophe also covered in his talk. (Also making me realise my colleague Jean Dolbeault in Dauphine was strongly involved in the theoretical analysis of PDMPs!) Then Samuel Power gave another perspective on PDMPs. With another augmentation, connected with time, what he calls trajectorial reversibility. This has the impact of diminishing the event rate, but creates some kind of reversibility which seems to go against the motivation for PDMPs. (Remember that all talks are available as videos on the BIRS webpage.) A remark in the talk worth reiterating is the importance of figuring out which kinds of approximations are acceptable in these approximations. Connecting somewhat with the next talk by Luc Rey-Bellet on a theory of robust approximations. In the sense of Poincaré, Gibbs, Bernstein, &tc. concentration inequalities and large deviations. With applications to rare events.The fourth and final “hand-on” session was run by Miranda Holmes-Certon on simulating under constraints. Motivated by research on colloids. For which the overdamp Langevin diffusion applies as an accurate model, surprisingly. Which makes a major change from the other talks [most of the workshop!] relying on this diffusion. (With an interesting intermede on molecular velcro made of DNA strands.) Connected with this example, exotic energy landscapes are better described by hard constraints. (Potentially interesting extension to the case when there are too many constraints to explore all of them?) Now, the definition of the measure projected on the manifold defined by the constraints is obviously an important step in simulating the distribution, which density is induced by the gradient of the constraints ∇q(x). The proposed algorithm is in the same spirit as the one presented by Tony the previous day, namely moving along the tangent space then on the normal space to get back to the manifold. A solution that causes issues when the gradient is (near) zero. A great hand-on session which induced massive feedback from the audience.

In the afternoon session, Gersende Fort gave a talk on a generalisation of the Wang-Landau algorithm, which modifies the true weights of the elements of a partition of the sampling space, to increase visits to low [probability] elements and jumps between modes. The idea is to rely on tempered versions of the original weights, learned by stochastic approximation. With an extra layer of adaptivity. Leading to an improvement with parameters that depends on the phase of the stochastic approximation. The second talk was by David Sanders on a recent paper in *Chaos* about importance sampling for rare events of (deterministic) billiard dynamics. With diffusive limits which tails are hard to evaluate, except by importance sampling. And the last talk of the day was by Anton Martinsson on simulated tempering for a molecular alignment problem. With weights of different temperatures proportional to the inverse of the corresponding normalising constants, which themselves can be learned by a form of bridge sampling if I got it right.

On a very minor note, I heard at breakfast a pretty good story from a fellow participant having to give a talk at a conference that was moved to a very early time in the morning due to an official appearing at a later time and as a result “enjoying” a very small audience to the point that a cleaning lady appeared and started cleaning the board as she could not conceive the talks had already started! Reminding me of this picture at IHP.

## computational statistics and molecular simulation [18w5023]

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags 18w5023, ABC, BIRS, Casa Matemática Oaxaca, CMO, computational statistics, crown of thorns, gerrymandering, HMC, killer robot, lead climbing, leapfrog integrator, Mexico, misspecified model, molecular dynamics, Monte Carlos Statistical Methods, Moreau-Yoshida, numerical integrator, overdamped Langevin algorithm, proximal optimisation, reversible jump MCMC, rock climbing, starfish, summary statistics, transferability, workshop on November 15, 2018 by xi'an **I** truly missed the gist of the first talk of the Wednesday morning of our X fertilisation workshop by Jianfeng Lu partly due to notations, although the topic very much correlated to my interests like path sampling, with an augmented version of HMC using an auxiliary indicator. And mentions made of BAOAB. Next, Marcello Pereyra spoke about Bayesian image analysis, with the difficulty of setting a prior on an image. In case of astronomical images there are motivations for an L¹ penalisation sparse prior. Sampling is an issue. Moreau-Yoshida proximal optimisation is used instead, in connection with our MCMC survey published in Stats & Computing two years ago. *Transferability* was a new concept for me, as introduced by Kerrie Mengersen (QUT), to extrapolate an estimated model to another system without using the posterior as a prior. With a great interlude about the crown of thorns starfish killer robot! Rather a prior determination based on historical data, in connection with recent (2018) Technometrics and Bayesian Analysis papers towards rejecting non-plausible priors. Without reading the papers (!), and before discussing the matter with Kerrie, here or in Marseille, I wonder at which level of precision this can be conducted. The use of summary statistics for prior calibration gave the approach an ABC flavour.

The hand-on session was Jonathan Mattingly’s discussion of gerrymandering reflecting on his experience at court! Hard to beat for an engaging talk reaching between communities. As it happens I discussed the original paper last year. Of course it was much more exciting to listen to Jonathan explaining his vision of the problem! Too bad I “had” to leave before the end for a [most enjoyable] rock climbing afternoon… To be continued at the dinner table! (Plus we got the complete explanation of the term gerrymandering, including this salamander rendering of the first identified as gerrymandered district!)