## postdoc at Warwick on robust SMC [call]

Posted in Kids, pictures, R, Statistics, University life with tags , , , , , , , , on January 11, 2020 by xi'an

Here is a call for a research fellow at the University of Warwick to work with Adam Johansen and Théo Damoulas on the EPSRC and Lloyds Register Foundaton funded project “Robust Scalable Sequential Monte Carlo with application to Urban Air Quality”. To quote

The position will be based primarily at the Department of Statistics of the University of Warwick. The post holder will work closely in collaboration with the rest of the project team and another postdoctoral researcher to be recruited shortly to work within the Data Centric Engineering programme at the Alan Turing Institute in London. The post holder will be expected to visit the Alan Turing Institute regularly.

Candidates with strong backgrounds in the mathematical analysis of stochastic algorithms or sequential Monte Carlo methods are particularly encouraged to apply. Closing date is 19 Jan 2020.

## estimating the marginal likelihood (or an information criterion)

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , on December 28, 2019 by xi'an

Tory Imai (from Kyoto University) arXived a paper last summer on what first looked like a novel approximation of the marginal likelihood. Based on the variance of thermodynamic integration. The starting argument is that there exists a power 0<t⁰<1 such that the expectation of the logarithm of the product of the prior by the likelihood to the power t⁰ or t⁰-powered likelihood  is equal to the standard log-marginal

$\log m(x) = \mathbb{E}^{t^0}[ \log f(X|\theta) ]$

when the expectation is under the posterior corresponding to the t⁰-powered likelihood (rather than the full likelihood). By an application of the mean value theorem. Watanabe’s (2013) WBIC replaces the optimum t⁰ with 1/log(n), n being the sample size. The issue in terms of computational statistics is of course that the error of WBIC (against the true log m(x)) is only characterised as an order of n.

The second part of the paper is rather obscure to me, as the motivation for the real log canonical threshold is missing, even though the quantity is connected with the power likelihood. And the DIC effective dimension. It then goes on to propose a new approximation of sBIC, where s stands for singular, of Drton and Plummer (2017) which I had missed (and may ask my colleague Martin later today at Warwick!). Quickly reading through the later however brings explanations about the real log canonical threshold being simply the effective dimension in Schwarwz’s BIC approximation to the log marginal,

$\log m(x) \approx= \log f(x|\hat{\theta}_n) - \lambda \log n +(m-1)\log\log n$

(as derived by Watanabe), where m is called the multiplicity of the real log canonical threshold. Both λ and m being unknown, Drton and Plummer (2017) estimate the above approximation in a Bayesian fashion, which leads to a double indexed marginal approximation for a collection of models. Since this thread leads me further and further from a numerical resolution of the marginal estimation, but brings in a different perspective on mixture Bayesian estimation, I will return to this highly  in a later post. The paper of Imai discusses a different numerical approximation to sBIC, With a potential improvement in computing sBIC. (The paper was proposed as a poster to BayesComp 2020, so I am looking forward discussing it with the author.)

## local mayhem, again and again and again…

Posted in Kids, pictures, Travel, University life with tags , , , , , , , , , , , , , , , , , , on December 27, 2019 by xi'an

The public transports in France and in particular in Paris have now been on strike for three weeks. In connection with a planned reform of the retirement conditions of workers with special status, like those in the train and metro companies, who can retire earlier than the legal age (62). As usual with social unrest in France, other categories joined the strike and the protest, including teachers and health service public workers, as well as police officers, fire-fighters and opera dancers, and even some students. Below are some figures from the OECD about average retirement conditions in nearby EU countries that show that these conditions are apparently better in France. (With the usual provision that these figures have been correctly reported.) In particular, the life expectancy at the start of retirement is the highest for both men and women. Coincidence (or not), my UCU affiliated colleagues in Warwick were also on strike a few weeks ago about their pensions…

Travelling through and around Paris by bike, I have not been directly affected by the strikes (as heavy traffic makes biking easier!), except for the morning of last week when I was teaching at ENSAE, when I blew up a tyre midway there and had to hop to the nearest train station to board the last train of the morning, arriving (only) 10mn late. Going back home was only feasible by taxi, which happened to be large enough to take my bicycle as well… Travelling to and from the airport for Vancouver and Birmingham was equally impossible by public transportation, meaning spending fair amounts of time in and money on taxis! And listening to taxi-drivers’ opinions or musical tastes. Nothing to moan about when considering the five to six hours spent by some friends of mine to get to work and back.

## summer internships at Warwick

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , , on December 16, 2019 by xi'an

## ABC for fish [PhD position]

Posted in Statistics with tags , , , , , , , on December 5, 2019 by xi'an

Richard Everitt (Warwick) is currently seeking a PhD candidate for working on approximate Bayesian computation methods, applied to Individual Based Models of fisheries, in collaboration with the government agency Centre for Environment, Fisheries and Aquaculture Science (CEFAS). Details on how to apply . More details can be found at the page of the doctoral training partnership (one can search for the project on this site). The application deadline is Friday, January 10, 2020, and it is open to UK and EU students.

## Bayesian probabilistic numerical methods

Posted in Books, pictures, Statistics, University life with tags , , , , , , on December 5, 2019 by xi'an

“…in isolation, the error of a numerical method can often be studied and understood, but when composed into a pipeline the resulting error structure maybe non-trivial and its analysis becomes more difficult. The real power of probabilistic numerics lies in its application to pipelines of numerical methods, where the probabilistic formulation permits analysis of variance (ANOVA) to understand the contribution of each discretisation to the overall numerical error.”

Jon Cockayne (Warwick), Chris Oates (formerly Warwick), T.J. Sullivan, and Mark Girolami (formerly Warwick) got their survey on Bayesian probabilistic numerical methods in the SIAM (Society for Industrial and Applied Mathematics) Review, which is quite a feat given the non-statistical flavour of the journal (although Art Owen is now one of the editors of the review). As already reported in some posts on the ‘Og, the concept relies on the construction of a prior measure over a set of potential solutions, and numerical methods are assessed against the associated posterior measure. Not only is this framework more compelling in a conceptual sense, but it also leads to novel probabilistic numerical methods managing to solve quite challenging numerical tasks. Congrats to the authors!

## what have rough paths got to do with data science?

Posted in Statistics with tags , , , , , , on November 22, 2019 by xi'an