**T**oday, two statisticians (and good friends of mine) from Australia, Noel Cressie and Kerrie Mengersen, got elected at the Australian Academy of Sciences. Congratulations to them!

an attempt at bloggin, nothing more…

**T**oday, two statisticians (and good friends of mine) from Australia, Noel Cressie and Kerrie Mengersen, got elected at the Australian Academy of Sciences. Congratulations to them!

**S**everal interesting entries in Le Monde Science & Médecine of this week (24 Jan 2018):

- This incredible report in the Journal of Ethnobiology of fire-spreading raptors, Black Kite, Whistling Kite, and Brown Falcon, who carry burning material to start fires further away and thus expose rodents and insects. This behaviour was already reported in some Aboriginal myths, as now backed up by independent observations.
- A report by Etienne Ghys of the opening of a new CNRS unit in mathematics in… London! The Abraham de Moivre Laboratory is one of the 36 mixed units located outside France to facilitate exchanges and collaborations. In the current case, in collaboration with Imperial. And as a mild antidote to Brexit and its consequences on exchanges between the UK and the EU. (When discussing Martin Hairer’s conference, Etienne forgot to mention his previous affiliation with Warwick.)
- A good-will-bad-stats article on the impact of increasing the number of urban bicycle trips to reduce the number of deaths. With the estimation that if 25% of the daily trips over 167 European (and British!) cities were done by bike, 10,000 deaths per year could be avoided! I have not read the original study, but I wonder at the true impact of this increase. If 25% of the commutes are made by bike, the remaining 75% are not and hence use polluting means of transportation. This means more citizens travelling by bike are exposed to the exhausts and fumes of cars, buses, trucks, &tc. Which should see an increase in respiratory diseases, including deaths, rather than a decrease. Unless this measure is associated with banning all exhaust emissions from cities, which does not sound a very likely outcome, even in Paris.
- An incoming happening at Cité internationale des Arts in Paris, on Feb 2-3, entitled “we are not the number we believe we are” (in French), based on the universe(s) of Ursula Le Guin who most sadly passed away the day the journal came out.
- A diffusion of urban riots in the suburbs of Paris in 2005 that closely follows epidemiological models of flu epidemics, using “a single sociological variable characterizing neighbourhood deprivation”. (Estimation of the SIR model is apparently done by maximum likelihood and model comparison by AIC, given the ODE nature of the models, ABC would have been quite appropriate for a Bayesian modelling!)

**M**y friends and co-authors David Frazier, Gael Martin, Brendan McCabe, and Worapree Maneesoonthorn arXived a paper on ABC forecasting at the turn of the year. ABC prediction is a natural extension of ABC inference in that, provided the full conditional of a future observation given past data and parameters is available but the posterior is not, ABC simulations of the parameters induce an approximation of the predictive. The paper thus considers the impact of this extension on the precision of the predictions. And argues that it is possible that this approximation is preferable to running MCMC in some settings. A first interesting result is that using ABC and hence conditioning on an insufficient summary statistic has no asymptotic impact on the resulting prediction, provided Bayesian concentration of the corresponding posterior takes place as in our convergence paper under revision.

“…conditioning inference about θ on η(y) rather than y makes no difference to the probabilistic statements made about [future observations]”

The above result holds both in terms of convergence in total variation and for proper scoring rules. Even though there is always a loss in accuracy in using ABC. Now, one may think this is a direct consequence of our (and others) earlier convergence results, but numerical experiments on standard time series show the distinct feature that, while the [MCMC] posterior and ABC posterior distributions on the parameters clearly differ, the predictives are more or less identical! With a potential speed gain in using ABC, although comparing parallel ABC versus non-parallel MCMC is rather delicate. For instance, a preliminary parallel ABC could be run as a burnin’ step for parallel MCMC, since all chains would then be roughly in the stationary regime. Another interesting outcome of these experiments is a case when the summary statistics produces a non-consistent ABC posterior, but still leads to a very similar predictive, as shown on this graph.This unexpected accuracy in prediction may further be exploited in state space models, towards producing particle algorithms that are greatly accelerated. Of course, an easy objection to this acceleration is that the impact of the approximation is unknown and un-assessed. However, such an acceleration leaves room for multiple implementations, possibly with different sets of summaries, to check for consistency over replicates.

Chris Drovandi sent me the information that the Statistics Group, QUT, Brisbane, is advertising for three positions:

- Professor in Statistical Data Science (Remuneration package from $AUD206,729 per year)
- Lecturer in Statistical Data Science (Remuneration package of $AUD108,796 to $AUD129,209 per year)
- PhD Scholarship in Computational Bayesian Statistics ($AUD35,000 per year tax-free for 3 years, with an additional $AUD5,000 per year for project costs)

This is a great opportunity, a very active group, and a great location, which I visited several times, so if interested apply before October 1.

**W**ith David Frazier and Judith Rousseau, we just arXived a paper studying the impact of a misspecified model on the outcome of an ABC run. This is a question that naturally arises when using ABC, but that has been not directly covered in the literature apart from a recently arXived paper by James Ridgway [that was earlier this month commented on the ‘Og]. On the one hand, ABC can be seen as a robust method in that it focus on the aspects of the assumed model that are translated by the [insufficient] summary statistics and their expectation. And nothing else. It is thus tolerant of departures from the hypothetical model that [almost] preserve those moments. On the other hand, ABC involves a degree of non-parametric estimation of the intractable likelihood, which may sound even more robust, except that the likelihood is estimated from pseudo-data simulated from the “wrong” model in case of misspecification.

In the paper, we examine how the pseudo-true value of the parameter [that is, the value of the parameter of the misspecified model that comes closest to the generating model in terms of Kullback-Leibler divergence] is asymptotically reached by some ABC algorithms like the ABC accept/reject approach and not by others like the popular linear regression [post-simulation] adjustment. Which suprisingly concentrates posterior mass on a completely different pseudo-true value. Exploiting our recent assessment of ABC convergence for well-specified models, we show the above convergence result for a tolerance sequence that decreases to the minimum possible distance [between the true expectation and the misspecified expectation] at a slow enough rate. Or that the sequence of acceptance probabilities goes to zero at the proper speed. In the case of the regression correction, the pseudo-true value is shifted by a quantity that does not converge to zero, because of the misspecification in the expectation of the summary statistics. This is not immensely surprising but we hence get a very different picture when compared with the well-specified case, when regression corrections bring improvement to the asymptotic behaviour of the ABC estimators. This discrepancy between two versions of ABC can be exploited to seek misspecification diagnoses, e.g. through the acceptance rate versus the tolerance level, or via a comparison of the ABC approximations to the posterior expectations of quantities of interest which should diverge at rate Vn. In both cases, ABC reference tables/learning bases can be exploited to draw and calibrate a comparison with the well-specified case.