Archive for University of Bristol

The Fry Building [Bristol maths]

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on March 7, 2020 by xi'an

While I had heard of Bristol maths moving to the Fry Building for most of the years I visited the department, starting circa 1999, this last trip to Bristol was the opportunity for a first glimpse of the renovated building which has been done beautifully, making it the most amazing maths department I have ever visited.  It is incredibly spacious and luminous (even in one of these rare rainy days when I visited), while certainly contributing to the cohesion and interactions of the whole department. And the choice of the Voronoi structure should not have come as a complete surprise (to me), given Peter Green’s famous contribution to their construction!

in Bristol for the day

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on February 28, 2020 by xi'an

I am in Bristol for the day, giving a seminar at the Department of Statistics where I had not been for quite a while (and not since the Department has moved to a beautifully renovated building). The talk is on ABC-Gibbs, whose revision is on the verge of being resubmitted. (I also hope Greta will let me board my plane tonight…)

research position in Bristol

Posted in pictures, Statistics, University life with tags , , , , , , , , , on September 6, 2019 by xi'an

Christophe Andrieu is seeking a senior research associate (reference ACAD103715) at the University of Bristol to work on new approaches to Bayesian data science. The selected candidate would work with Prof. Christophe Andrieu (School of Mathematics) and Prof. Mark Beaumont (Life Science) on new approaches to tackle Bayesian inference in complex statistical models arising in particular in the area of Health Science, with a focus on genetics and/or epidemiological aspects. The position is associated with a £3M programme funded by EPSRC, Bayes4Health, and brings together research groups from the Universities of Lancaster, Bristol, Cambridge, Oxford and Warwick. Active collaboration across the partner institutions, other project partners and the programme grant CoSInES is expected. The position is for up to four years.

The position is for a duration of four years and interviews will take place in early October. Applicants with strong methodological and computational skills and are looking to put together a team of researchers with skills that cover theoretical, methodological and applied statistics should contact Christophe Andrieu at the earliest.

p-values, Bayes factors, and sufficiency

Posted in Books, pictures, Statistics with tags , , , , , , , , , on April 15, 2019 by xi'an

Among the many papers published in this special issue of TAS on statistical significance or lack thereof, there is a paper I had already read before (besides ours!), namely the paper by Jonty Rougier (U of Bristol, hence the picture) on connecting p-values, likelihood ratio, and Bayes factors. Jonty starts from the notion that the p-value is induced by a transform, summary, statistic of the sample, t(x), the larger this t(x), the less likely the null hypothesis, with density f⁰(x), to create an embedding model by exponential tilting, namely the exponential family with dominating measure f⁰, and natural statistic, t(x), and a positive parameter θ. In this embedding model, a Bayes factor can be derived from any prior on θ and the p-value satisfies an interesting double inequality, namely that it is less than the likelihood ratio, itself lower than any (other) Bayes factor. One novel aspect from my perspective is that I had thought up to now that this inequality only holds for one-dimensional problems, but there is no constraint here on the dimension of the data x. A remark I presumably made to Jonty on the first version of the paper is that the p-value itself remains invariant under a bijective increasing transform of the summary t(.). This means that there exists an infinity of such embedding families and that the bound remains true over all such families, although the value of this minimum is beyond my reach (could it be the p-value itself?!). This point is also clear in the justification of the analysis thanks to the Pitman-Koopman lemma. Another remark is that the perspective can be inverted in a more realistic setting when a genuine alternative model M¹ is considered and a genuine likelihood ratio is available. In that case the Bayes factor remains smaller than the likelihood ratio, itself larger than the p-value induced by the likelihood ratio statistic. Or its log. The induced embedded exponential tilting is then a geometric mixture of the null and of the locally optimal member of the alternative. I wonder if there is a parameterisation of this likelihood ratio into a p-value that would turn it into a uniform variate (under the null). Presumably not. While the approach remains firmly entrenched within the realm of p-values and Bayes factors, this exploration of a natural embedding of the original p-value is definitely worth mentioning in a class on the topic! (One typo though, namely that the Bayes factor is mentioned to be lower than one, which is incorrect.)

mixture modelling for testing hypotheses

Posted in Books, Statistics, University life with tags , , , , , , , , , , on January 4, 2019 by xi'an

After a fairly long delay (since the first version was posted and submitted in December 2014), we eventually revised and resubmitted our paper with Kaniav Kamary [who has now graduated], Kerrie Mengersen, and Judith Rousseau on the final day of 2018. The main reason for this massive delay is mine’s, as I got fairly depressed by the general tone of the dozen of reviews we received after submitting the paper as a Read Paper in the Journal of the Royal Statistical Society. Despite a rather opposite reaction from the community (an admittedly biased sample!) including two dozens of citations in other papers. (There seems to be a pattern in my submissions of Read Papers, witness our earlier and unsuccessful attempt with Christophe Andrieu in the early 2000’s with the paper on controlled MCMC, leading to 121 citations so far according to G scholar.) Anyway, thanks to my co-authors keeping up the fight!, we started working on a revision including stronger convergence results, managing to show that the approach leads to an optimal separation rate, contrary to the Bayes factor which has an extra √log(n) factor. This may sound paradoxical since, while the Bayes factor  converges to 0 under the alternative model exponentially quickly, the convergence rate of the mixture weight α to 1 is of order 1/√n, but this does not mean that the separation rate of the procedure based on the mixture model is worse than that of the Bayes factor. On the contrary, while it is well known that the Bayes factor leads to a separation rate of order √log(n) in parametric models, we show that our approach can lead to a testing procedure with a better separation rate of order 1/√n. We also studied a non-parametric setting where the null is a specified family of distributions (e.g., Gaussians) and the alternative is a Dirichlet process mixture. Establishing that the posterior distribution concentrates around the null at the rate √log(n)/√n. We thus resubmitted the paper for publication, although not as a Read Paper, with hopefully more luck this time!