## Archive for University of Bristol

## a summer of British conferences!

Posted in pictures, Statistics, Travel, University life with tags BAYSM 2018, Britain, conference, Edinburgh, England, ISBA 2018, iwsm2018, statistical modelling, University of Bristol, Warwick on January 18, 2018 by xi'an## resampling methods

Posted in Books, pictures, Running, Statistics, Travel, University life with tags Book, Clifton, hidden Markov models, Hilbert curve, iterated importance sampling, resampling, sequential Monte Carlo, stratified resampling, systematic resampling, Université Paris Dauphine, University of Bristol on December 6, 2017 by xi'an**A** paper that was arXived [and that I missed!] last summer is a work on resampling by Mathieu Gerber, Nicolas Chopin (CREST), and Nick Whiteley. Resampling is used to sample from a weighted empirical distribution and to correct for very small weights in a weighted sample that otherwise lead to degeneracy in sequential Monte Carlo (SMC). Since this step is based on random draws, it induces noise (while improving the estimation of the target), reducing this noise is preferable, hence the appeal of replacing plain multinomial sampling with more advanced schemes. The initial motivation is for sequential Monte Carlo where resampling is rife and seemingly compulsory, but this also applies to importance sampling when considering several schemes at once. I remember discussing alternative schemes with Nicolas, then completing his PhD, as well as Olivier Cappé, Randal Douc, and Eric Moulines at the time (circa 2004) we were working on the Hidden Markov book. And getting then a somewhat vague idea as to why systematic resampling failed to converge.

In this paper, Mathieu, Nicolas and Nick show that stratified sampling (where a uniform is generated on every interval of length 1/n) enjoys some form of consistent, while systematic sampling (where the “same” uniform is generated on every interval of length 1/n) does not necessarily enjoy this consistency. There actually exists cases where convergence does not occur. However, a residual version of systematic sampling (where systematic sampling is applied to the residuals of the decimal parts of the n-enlarged weights) is itself consistent.

The paper also studies the surprising feature uncovered by Kitagawa (1996) that stratified sampling applied to an ordered sample brings an error of O(1/n²) between the cdf rather than the usual O(1/n). It took me a while to even understand the distinction between the original and the ordered version (maybe because Nicolas used the empirical cdf during his SAD (Stochastic Algorithm Day!) talk, ecdf that is the same for ordered and initial samples). And both systematic and deterministic sampling become consistent in this case. The result was shown in dimension one by Kitagawa (1996) but extends to larger dimensions via the magical trick of the Hilbert curve.

## more positions in the UK [postdoc & professor]

Posted in Statistics with tags academic position, Bristol, Britain, Durham, Durham university, England, Imperial College London, London, postdoctoral position, professor of statistics, United Kingdom, University of Bristol on October 13, 2017 by xi'an**I** have received additional emails from England advertising for positions in Bristol, Durham, and London, so here they are, with links to the complete advertising!

- The University of Bristol is seeking to appoint a number of Chairs in any areas of Mathematics or Statistical Science, in support of a major strategic expansion of the School of Mathematics. Deadline is December 4.
- Durham University is opening a newly created position of Professor of Statistics, with research and teaching duties. Deadline is November 6.
- Oliver Ratman, in the Department of Mathematics at Imperial College London, is seeking a Research Associate in Statistics and Pathogen Phylodynamics. Deadline is October 30.

## position in Bristol

Posted in pictures, Running, Statistics, Travel, University life with tags academic position, Bristol, England, lecturer, University of Bristol on October 4, 2017 by xi'an**T**here is [also] an opening for a Lecturer or Senior Lecture or Reader at the University of Bristol, with deadline 27th of November, 2017. The School of Mathematics and in particular the Institute for Statistical Science are quite active in research, with top rankings and a rich area of expertise domains, while [based on personal experience] the City of Bristol is a great place to live! (Details through the links.)

## position in Bristol

Posted in Statistics, University life with tags academic position, Bristol, Brunel, England, lecturer, School of Mathematics, University of Bristol on July 19, 2016 by xi'an**T**here is an opening for a Lecturer (i.e., assistant/associate professor) position in Statistical Science at the University of Bristol (School of Mathematics) with deadline August 7. Please contact Professor Christophe Andrieu for more details.

## read paper [in Bristol]

Posted in Books, pictures, Statistics, Travel, University life with tags Bayes factors, Bayesian hypothesis testing, Bayesian model choice, Bristol, cake, England, improper priors, mixtures of distributions, Neyman-Pearson, non-informative priors, parametrisation, Pima Indians, Read paper, seminar, University of Bristol on January 29, 2016 by xi'an**I** went to give a seminar in Bristol last Friday and I chose to present the testing with mixture paper. As we are busy working on the revision, I was eagerly looking for comments and criticisms that could strengthen this new version. As it happened, the (Bristol) Bayesian Cake (Reading) Club had chosen our paper for discussion, two weeks in a row!, hence the title!, and I got invited to join the group the morning prior to the seminar! This was, of course, most enjoyable and relaxed, including an home-made cake!, but also quite helpful in assessing our arguments in the paper. One point of contention or at least of discussion was the common parametrisation between the components of the mixture. Although all parametrisations are equivalent from a *single* component point of view, I can [almost] see why using a mixture with the same parameter value on all components may impose some unsuspected constraint on that parameter. Even when the parameter is *the same moment* for both components. This still sounds like a minor counterpoint in that the weight should converge to either zero or one and hence eventually favour the posterior on the parameter corresponding to the “true” model.

Another point that was raised during the discussion is the behaviour of the method under misspecification or for an M-open framework: when neither model is correct does the weight still converge to the boundary associated with the closest model (as I believe) or does a convexity argument produce a non-zero weight as it limit (as hinted by one example in the paper)? I had thought very little about this and hence had just as little to argue though as this does not sound to me like the primary reason for conducting tests. Especially in a Bayesian framework. If one is uncertain about both models to be compared, one should have an alternative at the ready! Or use a non-parametric version, which is a direction we need to explore deeper before deciding it is coherent and convergent!

A third point of discussion was my argument that mixtures allow us to rely on the same parameter and hence the same prior, whether proper or not, while Bayes factors are less clearly open to this interpretation. This was not uniformly accepted!

Thinking afresh about this approach also led me to broaden my perspective on the use of the posterior distribution of the weight(s) α: while previously I had taken those weights mostly as a proxy to the posterior probabilities, to be calibrated by pseudo-data experiments, as for instance in Figure 9, I now perceive them primarily as the portion of the data in agreement with the corresponding model [or hypothesis] and more importantly as a solution for staying away from a Neyman-Pearson-like decision. Or error evaluation. Usually, when asked about the interpretation of the output, my answer is to compare the behaviour of the posterior on the weight(s) with a posterior associated with a sample from each model. Which does sound somewhat similar to posterior predictives if the samples are simulated from the associated predictives. But the issue was not raised during the visit to Bristol, which possibly reflects on how unfrequentist the audience was [the Statistics group is], as it apparently accepted with no further ado the use of a posterior distribution as a soft assessment of the comparative fits of the different models. If not necessarily agreeing the need of conducting hypothesis testing (especially in the case of the Pima Indian dataset!).