**D**avid Frazier (Monash University) and Chris Drovandi (QUT) have recently come up with a robustness study of Bayesian synthetic likelihood that somehow mirrors our own work with David. In a sense, Bayesian synthetic likelihood is definitely misspecified from the start in assuming a Normal distribution on the summary statistics. When the data generating process is misspecified, even were the Normal distribution the “true” model or an appropriately converging pseudo-likelihood, the simulation based evaluation of the first two moments of the Normal is biased. Of course, for a choice of a summary statistic with limited information, the model can still be *weakly compatible* with the data in that there exists a pseudo-true value of the parameter θ⁰ for which the synthetic mean μ(θ⁰) is the mean of the statistics. (Sorry if this explanation of mine sounds unclear!) Or rather the Monte Carlo estimate of μ(θ⁰) coincidences with that mean.The same Normal toy example as in our paper leads to very poor performances in the MCMC exploration of the (unsympathetic) synthetic target. The robustification of the approach as proposed in the paper is to bring in an extra parameter to correct for the bias in the mean, using an additional Laplace prior on the bias to aim at sparsity. Or the same for the variance matrix towards inflating it. This over-parameterisation of the model obviously avoids the MCMC to get stuck (when implementing a random walk Metropolis with the target as a scale).

## Archive for Australia

## robust Bayesian synthetic likelihood

Posted in Statistics with tags ABC, Australia, Bayesian synthetic likelihood, Brisbane, industrial ruins, MCMC, Melbourne, Metropolis-Hastings algorithm, misspecified model, Monash University, pseudo-likelihood, QUT, summary statistics, Sydney Harbour on May 16, 2019 by xi'an## auxiliary likelihood ABC in print

Posted in Statistics with tags ABC, Australia, auxiliary likelihood, Bayesian econometrics, JCGS, Journal of Computational and Graphical Statistics, Melbourne, Monash University, Rimini on March 1, 2019 by xi'an**O**ur paper with Gael Martin, Brendan McCabe , David Frazier and Worapree Maneesoonthorn, with full title Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models, has now appeared in JCGS. To think that it started in Rimini in 2009, when I met Gael for the first time at the Rimini Bayesian Econometrics conference, although we really started working on the paper in 2012 when I visited Monash makes me realise the enormous investment we made in this paper, especially by Gael whose stamina and enthusiasm never cease to amaze me!

## risk-adverse Bayes estimators

Posted in Books, pictures, Statistics with tags Australia, dominating measure, f-divergence, Hellinger loss, intrinsic losses, invariance, Kullback-Leibler divergence, MAP estimators, Monash University, reparameterisation, Victoria on January 28, 2019 by xi'an**A**n interesting paper came out on arXiv in early December, written by Michael Brand from Monash. It is about risk-adverse Bayes estimators, which are defined as avoiding the use of loss functions (although why avoiding loss functions is not made very clear in the paper). Close to MAP estimates, they bypass the dependence of said MAPs on parameterisation by maximising instead π(θ|x)/√I(θ), which is invariant by reparameterisation if not by a change of dominating measure. This form of MAP estimate is called the Wallace-Freeman (1987) estimator [of which I never heard].

The formal definition of a *risk-adverse estimator* is still based on a loss function in order to produce a proper version of the probability to be “wrong” in a continuous environment. The difference between estimator and true value θ, as expressed by the loss, is enlarged by a scale factor k pushed to infinity. Meaning that differences not in the immediate neighbourhood of zero are not relevant. In the case of a countable parameter space, this is essentially producing the MAP estimator. In the continuous case, for “well-defined” and “well-behaved” loss functions and estimators and density, including an invariance to parameterisation as in my own intrinsic losses of old!, which the author calls *likelihood-based* loss function, mentioning f-divergences, the resulting estimator(s) is a Wallace-Freeman estimator (of which there may be several). I did not get very deep into the study of the convergence proof, which seems to borrow more from real analysis à la Rudin than from functional analysis or measure theory, but keep returning to the apparent dependence of the notion on the dominating measure, which bothers me.

## freedom to discriminate???

Posted in Statistics with tags Australia, blasphemy law, democracy index, discrimination, LGBT rights, Manif pour tous, religious freedom on November 18, 2018 by xi'an

“Gay students and teachers could be rejected by religious schools under changes to anti-discrimination laws being recommended by a federal review into religious freedom.” The Guardian, 9 Oct. 2018

The quote is not speaking of one of the 72 countries in the World where homosexuality is considered a crime (with 13 states applying the death penalty), but of Australia, ranked 8th on the Economist 2017 Democracy Index, where religious freedom arguments are legally recognised as a right to discriminate against homosexual students and staff. (As an aside, Australia still has a blasphemy law.)

“While the panel accepted the right of religious school to discriminate against students on the basis of gender identity or sexual orientation, it could see no justification for a school to discriminate on the basis of race, disability, pregnancy or intersex status.” The Sydney Morning Herald, 9 Oct. 2018

I find it flabbergasting that such newspeak inversions (also found in the French “Manif pour tous” slogans turning *égalité* into a discrimination argument against homosexual weddings and adoptions) can find their way into a legislative text. And more generally that religions can still continue to promote gender discrimination with no consequences.

## down-under ABC paper accepted in JCGS!

Posted in Books, pictures, Statistics, University life with tags ABC, Australia, auxiliary model, JCGS, journal, Journal of Computational and Graphical Statistics, Melbourne, Monash University, Mornington Peninsula, pinot gris, publication, state space model, Victoria wines on October 25, 2018 by xi'an**G**reat news!, the ABC paper we had originally started in 2012 in Melbourne with Gael Martin and Brendan MacCabe, before joining forces with David Frazier and Worapree Maneesoothorn, in expanding its scope to using auxiliary likelihoods to run ABC in state-space models, just got accepted in the Journal of Computational and Graphical Statistics. A reason to celebrate with a Mornington Peninsula Pinot Gris wine next time I visit Monash!

## statisticians at the Academy

Posted in pictures, University life with tags Australia, Australian Academy of Sciences, Kerrie Mengersen, Noel Cressie on May 22, 2018 by xi'an

**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!

## science tidbits

Posted in Books, Kids, pictures, Travel, University life with tags aborigines, Abraham De Moivre, Australia, bike path, CNRS, ethnobiology, hawk, kite, Le Monde, Martin Hairer, Queensland on January 28, 2018 by xi'an**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!)