Twenty-four PhD fellowships (“International Doctoral Training in Mathematical Sciences in France – MathPhDInFrance” co-funded by Marie Skłodowska-Curie Actions – HORIZON-MSCA-2022- COFUND) are available for the next academic year for a co-supervision between a laboratory in the Greater Paris region and another one in another French region. The applicants cannot have resided or carried out their main activity (work, studies, &c.) in France for more than 12 months in the three years immediately before the deadline of the call (i.e. between February 14th, 2021 and February 14th, 2024). They must be doctoral candidates, i.e. not yet awarded a doctoral degree by the deadline. Moreover, they must have a Master’s degree or an equivalent diploma at the time of their enrolment to PhD, in any domain of research in pure & applied mathematics, or theoretical computer science. The deadline is 14 February 2024 and applications do not require a confirmed supervisor at that time. (Obviously, feel free to contact me if interested.)
Archive for PhD thesis
24 PhD fellowships in Mathematical Sciences partly in Paris
Posted in Kids, Travel, University life with tags Île-de-France, Centre for Doctoral Training in Mathematics and Statistics, COFUND, Grand Palais, Invalides, Marie Skłodowska-Curie, MathPhDInFrance, Paris, PhD fellowship, PhD scholarship, PhD thesis on January 10, 2024 by xi'anAsymptotics of ABC when summaries converge at heterogeneous rates
Posted in pictures, Statistics, University life with tags ABC, Approximate Bayesian computation, Bayesian consistency, COVID-19, curse of dimensionality, lockdown, PhD thesis, summary statistics, Université Paris Dauphine, University of Oxford on November 21, 2023 by xi'an
We just posted a new arXival, jointly with Caroline Lawless, Judith Rousseau, and Robin Ryder. This is a significant component of Caroline’s PhD thesis in Oxford, on which we started working during the first COVID lockdown. In this paper, we extend our results with David Frazier, Gael Martin, both with whom I’ll soon be reunited!, and Judith, published in Biometrika in 2018, to the more challenging case where different components of the summary statistic vector converge to their respective means at different rates, with some possibly not even converging at all. While this sounds impossible (!), we do prove consistency of the ABC posterior under such heterogeneous rates.
Wentao Li and Paul Fearnhead (also in Biometrika and in 2018) reduce the curse of the dimension of the set of summary statistic by showing, in the specific case of asymptotically normal summary statistics concentrating at the same rate, that a local linear post-processing step leads to a significant improvement in the theoretical behaviour of the ABC posterior. However, due to this focus on reducing the impact of the dimension of the summary statistics, it is therefore important to study its efficiency in a context where the summary statistics are not as well behaved. Surprinsingly maybe, we show that the significant improvement due to local linear post-processing persists even when summary statistics have heterogeneous behaviour. Most interestingly, the number of summary statistics which converge at the fast rate has no impact on the rate of posterior concentration nor on the shape of the ABC posterior (provided it exceeds the dimension of the parameter).
Adrian’s defence
Posted in Statistics with tags Bayes factor, Dirichlet mixture priors, mixtures, PhD thesis, PSL, thesis defence, Université Paris Dauphine on November 10, 2023 by xi'an
Bayesian inference and conformal prediction
Posted in Books, Kids, Statistics, University life with tags AISTATS 2021, École Polytechnique, Bayesian inference, conformal prediction, differential privacy, distributed Bayesian inference, federated learning, ICML 2023, large scale inference, Paris-Saclay campus, PhD thesis, thesis defence, uncertainty quantification on October 10, 2023 by xi'an
insufficient Gibbs sampling
Posted in Books, Kids, Statistics, University life with tags ABC, arXiv, boar, CIRM, George Casella, Gibbs sampling, insufficiency, latent variable, Luminy campus, mad, median, PhD thesis, poster session, Université Paris Dauphine on July 29, 2023 by xi'an
We have just arXived our paper on insufficient Gibbs sampling with Antoine Luciano and Robin Ryder, from Université Paris Dauphine. This is Antoine’s first paper and part of his PhD. (In particular, he wrote the entire code.) The idea stemmed from a discussion on ABC benchmarks, like the one when the pair (median, MAD) is the only available observation. With no available joint density, the setting seems to prohibit calling for an MCMC sampler. However, simulating the complete data set conditional on these statistics proves feasible, with a bit of bookkeeping. With obviously much better results [demonstrated above for a Cauchy example] than when calling ABC and at a very similar cost. (If not accounting for the ability of ABC to be parallelised.) The idea can be extended to other settings, obviously, as long as completion remains achievable. (And a big thanks to our friend Ed George who suggested the title, while at CIRM. I had suggested “Gibbs for boars” as a poster title, in connection with the historical time-line of
Gibbs for Kids (Casella and George) — Gibbs for Pigs (Gianola) — Gibbs for Robust Pigs = Gibbs for Boars
and the abundance of boars on the Luminy campus, but this did not sound convincing enough for Antoine.)
