Archive for asymptotic Bayesian methods

Big Bayes postdoctoral position in Oxford [UK]

Posted in Statistics with tags , , , , , , , , , , , on March 3, 2022 by xi'an

Forwarding a call for postdoctoral applications from Prof Judith Rousseau, with deadline 30 March:

Seeking a Postdoctoral Research Assistant, to join our group at the Department of Statistics. The Postdoctoral Research Assistant will be carrying out research for the ERC project General Theory for Big Bayes, reporting to Professor Judith Rousseau. They will provide guidance to junior members of the research group such as PhD students, and/or project volunteers.

The aim of this project is to develop a general theory for the analysis of Bayesian methods in complex and high (or infinite) dimensional models which will cover not only fine understanding of the posterior distributions but also an analysis of the output of the algorithms used to implement the approaches. The main objectives of the project are (briefly): 1) Asymptotic analysis of the posterior distribution of complex high dimensional models 2) Interactions between the asymptotic theory of high dimensional posterior distributions and computational complexity. We will also enrich these theoretical developments by 3) strongly related domains of applications, namely neuroscience, terrorism and crimes, and ecology.

The postholder will hold or be close to completion of a PhD/DPhil in statistics together with relevant experience. They will have the ability to manage own academic research and associated activities and have previous experience of contributing to publications/presentations. They will contribute ideas for new research projects and research income generation. Ideally, the postholder will also have experience in theoretical properties of Bayesian procedures and/or approximate Bayesian methods.

did variational Bayes work?

Posted in Books, Statistics with tags , , , , , , , , , on May 2, 2019 by xi'an

An interesting ICML 2018 paper by Yuling Yao, Aki Vehtari, Daniel Simpson, and Andrew Gelman I missed last summer on [the fairly important issue of] assessing the quality or lack thereof of a variational Bayes approximation. In the sense of being near enough from the true posterior. The criterion that they propose in this paper relates to the Pareto smoothed importance sampling technique discussed in an earlier post and which I remember discussing with Andrew when he visited CREST a few years ago. The truncation of the importance weights of prior x likelihood / VB approximation avoids infinite variance issues but induces an unknown amount of bias. The resulting diagnostic is based on the estimation of the Pareto order k. If the true value of k is less than ½, the variance of the associated Pareto distribution is finite. The paper suggests to conclude at the worth of the variational approximation when the estimate of k is less than 0.7, based on the empirical assessment of the earlier paper. The paper also contains a remark on the poor performances of the generalisation of this method to marginal settings, that is, when the importance weight is the ratio of the true and variational marginals for a sub-vector of interest. I find the counter-performances somewhat worrying in that Rao-Blackwellisation arguments make me prefer marginal ratios to joint ratios. It may however be due to a poor approximation of the marginal ratio that reflects on the approximation and not on the ratio itself. A second proposal in the paper focus on solely the point estimate returned by the variational Bayes approximation. Testing that the posterior predictive is well-calibrated. This is less appealing, especially when the authors point out the “dissadvantage is that this diagnostic does not cover the case where the observed data is not well represented by the model.” In other words, misspecified situations. This potential misspecification could presumably be tested by comparing the Pareto fit based on the actual data with a Pareto fit based on simulated data. Among other deficiencies, they point that this is “a local diagnostic that will not detect unseen modes”. In other words, what you get is what you see.

congrats, Prof Rousseau!

Posted in Statistics with tags , , , , , , , , on April 4, 2019 by xi'an

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