Archive for QUT

Pitman medal for Kerrie Mengersen

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on December 20, 2016 by xi'an

6831250-3x2-700x467My friend and co-author of many years, Kerrie Mengersen, just received the 2016 Pitman Medal, which is the prize of the Statistical Society of Australia. Congratulations to Kerrie for a well-deserved reward of her massive contributions to Australian, Bayesian, computational, modelling statistics, and to data science as a whole. (In case you wonder about the picture above, she has not yet lost the medal, but is instead looking for jaguars in the Amazon.)

This medal is named after EJG Pitman, Australian probabilist and statistician, whose name is attached to an estimator, a lemma, a measure of efficiency, a test, and a measure of comparison between estimators. His estimator is the best equivariant (or invariant) estimator, which can be expressed as a Bayes estimator under the relevant right Haar measure, despite having no Bayesian motivation to start with. His lemma is the Pitman-Koopman-Darmois lemma, which states that outside exponential families, sufficient is essentially useless (except for exotic distributions like the Uniform distributions). Darmois published the result first in 1935, but in French in the Comptes Rendus de l’Académie des Sciences. And the measure of comparison is Pitman nearness or closeness, on which I wrote a paper with my friends Gene Hwang and Bill Strawderman, paper that we thought was the final paper on the measure as it was pointing out several majors deficiencies with this concept. But the literature continued to grow after that..!

Jeff down-under

Posted in Books, Statistics, Travel, University life with tags , , , , , , , on September 9, 2016 by xi'an

amsi_ssaJeff Rosenthal is the AMSI-SSA (Australia Mathematical Sciences Institute – Statistical Society of Australia) lecturer this year and, as I did in 2012, will tour Australia giving seminars. Including this one at QUT. Enjoy, if you happen to be down-under!

statistics with jaguars

Posted in pictures, Statistics, Travel, University life with tags , , , on April 8, 2016 by xi'an
Following a field trip to Péru of my friend Kerrie Mengersen and other researchers from QUT, to study jaguar population, The Australian ran a story about this most exotic expedition. (Although Kerrie is familiar with exotic topics, since she also worked on cheetahs in Africa and orang-utans in Indonesia.) While the newspaper does not get into the details of the mathematical model used to describe the jaguar population, it turns quite lyrical about the expedition itself and the interactions with the local human populations. In the end it does not sound that terrible that the group could not see any jaguar, despite evidence of a strong presence in the area, as everyone came back unscathed!

scalable Bayesian inference for the inverse temperature of a hidden Potts model

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , on April 7, 2015 by xi'an

Brisbane, summer 2008Matt Moores, Tony Pettitt, and Kerrie Mengersen arXived a paper yesterday comparing different computational approaches to the processing of hidden Potts models and of the intractable normalising constant in the Potts model. This is a very interesting paper, first because it provides a comprehensive survey of the main methods used in handling this annoying normalising constant Z(β), namely pseudo-likelihood, the exchange algorithm, path sampling (a.k.a., thermal integration), and ABC. A massive simulation experiment with individual simulation times up to 400 hours leads to select path sampling (what else?!) as the (XL) method of choice. Thanks to a pre-computation of the expectation of the sufficient statistic E[S(Z)|β].  I just wonder why the same was not done for ABC, as in the recent Statistics and Computing paper we wrote with Matt and Kerrie. As it happens, I was actually discussing yesterday in Columbia of potential if huge improvements in processing Ising and Potts models by approximating first the distribution of S(X) for some or all β before launching ABC or the exchange algorithm. (In fact, this is a more generic desiderata for all ABC methods that simulating directly if approximately the summary statistics would being huge gains in computing time, thus possible in final precision.) Simulating the distribution of the summary and sufficient Potts statistic S(X) reduces to simulating this distribution with a null correlation, as exploited in Cucala and Marin (2013, JCGS, Special ICMS issue). However, there does not seem to be an efficient way to do so, i.e. without reverting to simulating the entire grid X…

Pre-processing for approximate Bayesian computation in image analysis

Posted in R, Statistics, University life with tags , , , , , , , , , , , , , on March 21, 2014 by xi'an

ridge6With Matt Moores and Kerrie Mengersen, from QUT, we wrote this short paper just in time for the MCMSki IV Special Issue of Statistics & Computing. And arXived it, as well. The global idea is to cut down on the cost of running an ABC experiment by removing the simulation of a humongous state-space vector, as in Potts and hidden Potts model, and replacing it by an approximate simulation of the 1-d sufficient (summary) statistics. In that case, we used a division of the 1-d parameter interval to simulate the distribution of the sufficient statistic for each of those parameter values and to compute the expectation and variance of the sufficient statistic. Then the conditional distribution of the sufficient statistic is approximated by a Gaussian with these two parameters. And those Gaussian approximations substitute for the true distributions within an ABC-SMC algorithm à la Del Moral, Doucet and Jasra (2012).

residuals

Across 20 125 × 125 pixels simulated images, Matt’s algorithm took an average of 21 minutes per image for between 39 and 70 SMC iterations, while resorting to pseudo-data and deriving the genuine sufficient statistic took an average of 46.5 hours for 44 to 85 SMC iterations. On a realistic Landsat image, with a total of 978,380 pixels, the precomputation of the mapping function took 50 minutes, while the total CPU time on 16 parallel threads was 10 hours 38 minutes. By comparison, it took 97 hours for 10,000 MCMC iterations on this image, with a poor effective sample size of 390 values. Regular SMC-ABC algorithms cannot handle this scale: It takes 89 hours to perform a single SMC iteration! (Note that path sampling also operates in this framework, thanks to the same precomputation: in that case it took 2.5 hours for 10⁵ iterations, with an effective sample size of 10⁴…)

Since my student’s paper on Seaman et al (2012) got promptly rejected by TAS for quoting too extensively from my post, we decided to include me as an extra author and submitted the paper to this special issue as well.

Bayesian inference for low count time series models with intractable likelihoods

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , on January 21, 2014 by xi'an

sunset over the Brisbane river, Australia, Aug. 17, 2012Last evening, I read a nice paper with the above title by Drovandi, Pettitt and McCutchan, from QUT, Brisbane. Low count refers to observation with a small number of integer values. The idea is to mix ABC with the unbiased estimators of the likelihood proposed by Andrieu and Roberts (2009) and with particle MCMC… And even with a RJMCMC version. The special feature that makes the proposal work is that the low count features allows for a simulation of pseudo-observations (and auxiliary variables) that may sometimes authorise an exact constraint (that the simulated observation equals the true observation). And which otherwise borrows from Jasra et al. (2013) “alive particle” trick that turns a negative binomial draw into an unbiased estimation of the ABC target… The current paper helped me realise how powerful this trick is. (The original paper was arXived at a time I was off, so I completely missed it…) The examples studied in the paper may sound a wee bit formal, but they could lead to a better understanding of the method since alternatives could be available (?). Note that all those examples are not ABC per se in that the tolerance is always equal to zero.

The paper also includes reversible jump implementations. While it is interesting to see that ABC (in the authors’ sense) can be mixed with RJMCMC, it is delicate to get a feeling about the precision of the results, without a benchmark to compare to. I am also wondering about less costly alternatives like empirical likelihood and other ABC alternatives. Since Chris is visiting Warwick at the moment, I am sure we can discuss this issue next week there.

generalised Savage-Dickey ratio

Posted in Statistics, University life with tags , , , , , , , , on November 11, 2013 by xi'an

KONICA MINOLTA DIGITAL CAMERAToday, Ewan Cameron arXived a paper that generalises our Robert and Marin (2010) paper on the measure theoretic difficulties (or impossibilities) of the Savage-Dickey ratio and on the possible resolutions. (A paper of mine’s I like very much despite it having neither impact nor quotes, whatsoever! Until this paper.) I met Ewan last year when he was completing a PhD with Tony Pettitt at QUT in astrostatistics, but he also worked did not work on this transdimensional ABC algorithm with application to worm invasion in Northern Alberta (arXive I reviewed last week)… Ewan also runs a blog called Another astrostatistics blog, full of goodies, incl. the one where he announces he moves to… zoology in Oxford! Anyway, this note extends our paper and a mathematically valid Savage-Dickey ratio representation to the case when the posterior distributions have no density against the Lebesgue measure. For instance for Dirichlet processes or Gaussian processes priors. Using generic Radon-Nykodim derivatives instead. The example is somewhat artificial, superimposing a Dirichlet process prior onto the Old faithful benchmark. But this is an interesting entry, worth mentioning, into the computation of Bayes factors. And the elusive nature of the Savage-Dickey ratio representation.