*“One of our contribution comes from the mathematical analysis of the consequence of conditioning the parameters of interest on consistent statistics and intrinsically inconsistent statistics”*

Xiaolong Zhong and Malay Ghosh have just arXived an ABC paper focussing on the convergence of the method. And on the use of sufficient dimension reduction techniques for the construction of summary statistics. I had not heard of this approach before so read the paper with interest. I however regret that the paper does not link with the recent consistency results of Liu and Fearnhead and of Daniel Frazier, Gael Martin, Judith Rousseau and myself. When conditioning upon the MLE [or the posterior mean] as the summary statistic, Theorem 1 states that the Bernstein-von Mises theorem holds, missing a limit in the tolerance ε. And apparently missing conditions on the speed of convergence of this tolerance to zero although the conditioning event involves the true value of the parameter. This makes me wonder at the relevance of the result. The part about partial posteriors and the characterisation of limiting posterior distributions stats with the natural remark that the mean of the summary statistic must identify the whole parameter θ to achieve consistency, a point central to our 2014 JRSS B paper. The authors suggest using a support vector machine to derive the summary statistics, an idea already exploited by Heiko Strathmann et al.. There is no consistency result of relevance for ABC in that second and final part, which ends up rather abruptly. Overall, while the paper contributes to the current reflection on the convergence properties of ABC, the lack of scaling of the tolerance ε calls for further investigations.

*[Disclaimer: I am not involved in handling this paper as an AE or as a referee for the Annals of Statistics!]*

Filed under: Statistics, University life Tagged: ABC, ABC validation, consistency, sufficiency, summary statistics, tolerance ]]>

“In this study, we show that formulating a dynamical system as a general hierarchical state-space model enables us to independently estimate the model evidence for each model class.”

Subset simulation is a nested technique that produces a sequence of nested balls (and related tolerances) such that the conditional probability to be in the next ball given the previous one remains large enough. Requiring a new round of simulation each time. This is somewhat reminding me of nested sampling, even though the two methods differ. For subset simulation, estimating the level probabilities means that there also exists a converging (and even unbiased!) estimator for the evidence associated with different tolerance levels. Which is not a particularly natural object unless one wants to turn it into a tolerance selection principle, which would be quite a novel perspective. But not one adopted in the paper, seemingly. Given that the application section truly compares models I must have missed something there. (Blame the long flight from San Francisco to Sydney!) Interestingly, the different models as in Table 4 relate to different tolerance levels, which may be an hindrance for the overall validation of the method.

I find the subsequent part on getting rid of uncertain prediction error model parameters of lesser [personal] interest as it essentially replaces the marginal posterior on the parameters of interest by a BIC approximation, with the unsurprising conclusion that “the prior distribution of the nuisance parameter cancels out”.

Filed under: Books, Statistics, Travel Tagged: ABC, Bayesian model comparison, BIC, evidence, hidden Markov models, Laplace approximation, nested sampling, San Francisco, subset simulation, Sydney Harbour ]]>

I started with the cell, which is a 17 pages book with a few dozen sentences, and one or more pictures per page. Pictures drawn in a sort of naïve fashion that should appeal to young children. Being decades away from being a kid and more than a decade away from raising a kid (happy 20th birthday, Rachel!), I have trouble assessing the ideal age of the readership or the relevance of introducing to them [all] 13 components of an animal cell, from the membrane to the cytoplasm. Mentioning RNA and DNA without explaining what it is. Each of these components gets added to the cell picture as it comes, with a one line description of its purpose. I wonder how much a kid can remember of this list, while (s)he may wonder where those invisible cells stand. And why they are for. (When checking on Google, I found this sequence of pages more convincing, if much more advanced. Again, I am not the best suited for assessing how kids would take it!)

The 21 pages book about the neurons is more explanatory than descriptive and I thus found it more convincing (again with not much of an idea of how a kid would perceive it!). It starts from the brain sending signals, to parts of the body and requiring a medium to do so, which happens to be made of neurons. Once again, though, I feel the book spends too much time on the description rather than on the function of the neurons, e.g., with no explanation of how the signal moves from the brain to the neuron sequence or from the last neuron to the muscle involved.

The (young) scientist notebook is the best book in the series in my opinion: it reproduces a lab book and helps a young kid to formalise what (s)he thinks is a scientific experiment. As a kid, I did play at conducting “scientific” “experiments” with whatever object I happened to find, or later playing with ready-made chemistry and biology sets, but having such a lab book would have been terrific! Setting the question of interest and the hypothesis or hypotheses behind it prior to running the experiment is a major lesson in scientific thinking that should be offered to every kid! However, since it contains no pictures but mostly blank spaces to be filled by the young reader, one could suggest to parents to print such lab report sheets themselves.

Filed under: Books, Kids Tagged: biologie 2000, book review, cell, chimie 2000, neuron, notebook, scientific experiments, scientific mind, Think-A-Lot-Tots, Thomai Dion ]]>

Filed under: Books Tagged: Arturo Pérez-Reverte, Dos de Mayo, French history, Joachim Murat, Madrid, Napoléon Bonaparte, Spain, Spanish history, un dià de cólera ]]>

Filed under: pictures, Statistics, Travel, University life, Wines Tagged: ABC, ABC convergence, asymptotic normality, Australia, consistency, Melbourne, Monash University, Qantas, San Francisco, Yarra river ]]>

Filed under: Kids, pictures, Travel Tagged: AMTRAK, California, Sacramento, train, USA, vacations ]]>

The next session of the morning was another instance of conflicting talks and I hoped from one room to the next to listen to Hani Doss’s empirical Bayes estimation with intractable constants (where maybe SAME could be of interest), Youssef Marzouk’s transport maps for MCMC, which sounds like an attractive idea provided the construction of the map remains manageable, and Paul Russel’s adaptive importance sampling that somehow sounded connected with our population Monte Carlo approach. (With the additional step of considering transform maps.)

An interesting item of information I got from the final announcements at MCqMC 2016 just before heading to Monash, Melbourne, is that MCqMC 2018 will take place in the city of Rennes, Brittany, on July 2-6. Not only it is a nice location on its own, but it is most conveniently located in space and time to attend ISBA 2018 in Edinburgh the week after! Just moving from one Celtic city to another Celtic city. Along with other planned satellite workshops, this occurrence should make ISBA 2018 more attractive [if need be!] for participants from oversea.

Filed under: Mountains, pictures, Running, Statistics, Travel, University life Tagged: Brittany, California, conference, Edinburgh, MCMC, MCqMC 2016, Monte Carlo Statistical Methods, population Monte Carlo, pseudo-marginal MCMC, quadrangle, quasi-Monte Carlo methods, Rennes, Scotland, simulation, Stanford University ]]>

Filed under: Kids, Wines Tagged: German wines, Riesling, white wines ]]>

The following session was a nightmare in that I wanted to attend all four at once! I eventually chose the transport session, in particular because Xiao-Li advertised it at the end of my talk. The connection is that his warp bridge sampling technique provides a folding map between modes of a target. Using a mixture representation of the target and folding all components to a single distribution. Interestingly, this transformation does not require a partition and preserves the normalising constants [which has a side appeal for bridge sampling of course]. In a problem with an unknown number of modes, the technique could be completed by [our] folding in order to bring the unobserved modes into the support of the folded target. Looking forward the incoming paper! The last talk of this session was by Matti Vihola, connecting multi-level Monte Carlo and unbiased estimation à la Rhee and Glynn, paper that I missed when it got arXived last December.

The last session of the day was about probabilistic numerics. I have already discussed extensively about this approach to numerical integration, to the point of being invited to the NIPS workshop as a skeptic! But this was an interesting session, both with introductory aspects and with new ones from my viewpoint, especially Chris Oates’ description of a PN method for handling both integrand and integrating measure as being uncertain. Another arXival that went under my decidedly deficient radar.

Filed under: Books, pictures, Statistics, Travel, University life Tagged: folded Markov chain, Hermann Weyl, MCqMC 2016, multi-level Monte Carlo, NIPS 2015, probabilistic numerics, Stanford University, unbiased estimation, warped bridge sampling ]]>

Filed under: pictures, Running, Travel Tagged: blue, California, Capital, city, Sacramento, skyscrapers, summer, USA, vacations ]]>