Archive for PhD students
why don’t you wear a suit?!
Posted in Books, Kids, pictures, Travel, University life with tags baby Trump, black Friday, CDT, Centre for Doctoral Training, department of statistics, Des Moines, French Navy, Iowa, John Cairns, journalism, MAGA, objectivity, Oxford, OxWaSP, PhD students, Racoon River Brewing Co., Solidarity with Ukraine, Trump administration, University of Oxford, US politics, USA, Volodymyr Zelenskiy, White House on March 4, 2025 by xi'an
important and published [Markov chains]
Posted in Books, Statistics, University life with tags Bernoulli society, CLT, geometric ergodicity, importance sampling, Law of Large Numbers, Markov kernel, MCMC, modes of a mixture, PhD students, residual sampling, semi-Markov chain, SPA, stochastic processes and their applications, vanilla Rao-Blackwellisation on February 26, 2024 by xi'an
Our importance Markov chain paper (with Charly Andral (PhD, Paris Dauphine), Randal Douc, and Hugo Marival (PhD, Telecom SudParis) has been published (on-line) by stochastic processes and their applications (SPA). Incidentally, my first publication in this journal. To paraphrase its abstract, it sort of bridges the (unsuspected?) gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain targeting an instrumental distribution (typically via a MCMC kernel), rather than the target of interest, the Importance Markov chain produces an extended Markov chain whose (first) marginal distribution converges to said target distribution. For instance, when targeting a multimodal distribution, the instrumental distribution can be chosen as a tempered version of the target and this frees the algorithm to explore its multiple modal regions more efficiently. We also derive a Law of Large Numbers and a Central Limit Theorem as well as prove geometric ergodicity for this extended kernel under mild assumptions on the instrumental kernel. Computationally, the algorithm is easy to implement and preexisting librairies can be used to sample from the instrumental distribution.
Nature snapshots [10 November]
Posted in Books, Kids, Travel, University life with tags Black Death, book reviews, Coventry, COVID-19, DNA, graduates, Indian politics, Julian Huxley, London, natural selection, Nature, PhD students, Sally Clark, sheep on December 11, 2022 by xi'an
- India (federal) government scapping nearly 300 science awards this year
- a re-analysis of a sudden infant death conviction in Australia relying on rare genetic mutations rather than statistics (as in Sally Clark’s case)
- a book review about a story of the Huxley family that made me realise I had confused most of them as a single person
- a DNA analysis of Black Death survivors (in both London and Denmark), showing natural selection occurred very quickly during the pandemic and increased the risk of autoimmune diseases
- a genuine design of experiment that demonstrated that light grazing by sheep increases diversity, while fertilization does not
- an astronomy paper on cooling supernovae using Bayes factors
- an attempt at rationalising the answer to the Covid threat involving a large panel of experts (and my colleague Miquel Olui-Barton as a co-author)
- a pessimistic assessment by graduate students of their career prospects
Blackwell-Rosenbluth Award deadline extended to 7 August 2022
Posted in pictures, Statistics, University life with tags Arianna Rosenbluth, Blackwell-Rosenbluth Award, David Blackwell, fencing, PhD students on July 30, 2022 by xi'an
The deadline for submission of a nomination for the Blackwell-Rosenbluth j-ISBA Award is now 7 August. Ph.D. students or early career researchers who obtained their PhD after January 1, 2017 are eligible for nomination. A nomination may come from any ISBA member, including the nominee themselves.
important Markov chains
Posted in Books, Statistics, University life with tags arXiv, CLT, geometric ergodicity, importance sampling, Law of Large Numbers, Markov kernel, MCMC, PhD students, residual sampling, semi-Markov chain, Université Paris Dauphine, vanilla Rao-Blackwellisation on July 21, 2022 by xi'an
With Charly Andral (PhD, Paris Dauphine), Randal Douc, and Hugo Marival (PhD, Telecom SudParis), we just arXived a paper on importance Markov chains that merges importance sampling and MCMC. An idea already mentioned in Hastings (1970) and even earlier in Fodsick (1963), and later exploited in Liu et al. (2003) for instance. And somewhat dual of the vanilla Rao-Backwellisation paper Randal and I wrote a (long!) while ago. Given a target π with a dominating measure π⁰≥Mπ, using a Markov kernel to simulate from this dominating measure and subsampling by the importance weight ρ does produce a new Markov chain with the desired target measure as invariant distribution. However, the domination assumption is rather unrealistic and a generic approach can be implemented without it, by defining an extended Markov chain, with the addition of the number N of replicas as the supplementary term… And a transition kernel R(n|x) on N with expectation ρ, which is a minimal(ist) assumption for the validation of the algorithm.. While this initially defines a semi-Markov chain, an extended Markov representation is also feasible, by decreasing N one by one until reaching zero, and this is most helpful in deriving convergence properties for the resulting chain, including a CLT. While the choice of the kernel R is free, the optimal choice is associated with residual sampling, where only the fractional part of ρ is estimated by a Bernoulli simulation.
