The wiki on objective, reference, vague, neutral [or whichever label one favours] priors that was suggested at the previous O’Bayes meeting in Valencià, was introduced as Wikiprevia by Gonzalo Garcia-Donato. It aims at classifying recommended priors in most of the classical models, along with discussion panels, and it should soon get an official launch, when contributors will be welcome to include articles in a wiki principle. I wish the best to this venture which, I hope, will induce O’Bayesians to contribute actively.

In a brilliant talk that quickly reverted my jetlag doziness, Peter Grünwald returned to the topic he presented last year in Sardinia, namely safe Bayes or powered-down likelihoods to handle some degree of misspecification, with a further twist of introducing an impossible value `o’ that captures missing mass (to be called Peter’s demon?!), which absolute necessity I did not perceive. Food for thoughts, definitely. (But I feel that the only safe Bayes is the dead Bayes, as protecting against all kinds of mispecifications means no action is possible.)

I also appreciated Cristiano Villa’s approach to constructing prior weights in model comparison from a principled and decision-theoretic perspective even though I felt that the notion of ranking parameter importance required too much input to be practically feasible. (Unless I missed that point.)

Laura Ventura gave her talk on using for ABC various scores or estimating equations as summary statistics, rather than the corresponding M-estimators, which offers the appealing feature of reducing computation while being asymptotically equivalent. (A feature we also exploited for the regular score function in our ABC paper with Gael, David, Brendan, and Wonapree.) She mentioned the Hyvärinen score [of which I first heard in Padova!] as a way to bypass issues related to doubly intractable likelihoods. Which is a most interesting proposal that bypasses (ABC) simulations from such complex targets by exploiting a pseudo-posterior.

Veronika Rockova presented a recent work on concentration rates for regression tree methods that produce a rigorous analysis of these methods. Showing that the spike & slab priors plus BART [equals spike & tree] achieve sparsity and optimal concentration. In an oracle sense. With a side entry on assembling partition trees towards creating a new form of BART. Which made me wonder whether or not this was also applicable to random forests. Although they are not exactly Bayes. Demanding work in terms of the theory behind but with impressive consequences!

Just before I left O’Bayes 17 for Houston airport, Nick Polson, along with Peter McCullach, proposed an intriguing notion of sparse Bayes factors, which corresponds to the limit of a Bayes factor when the prior probability υ of the null goes to zero. When the limiting prior is replaced with an exceedance measure that can be normalised into a distribution, but does it make the limit a special prior? Linking υ with the prior under the null is not an issue (this was the basis of my 1992 Lindley paradox paper) but the sequence of priors indexed by υ need be chosen. And reading from the paper at Houston airport, I could not spot a construction principle that would lead to a reference prior of sorts. One thing that Nick mentioned during his talk was that we observed directly realisations of the data marginal, but this is generally not the case as the observations are associated with a given value of the parameter, not one for each observation.The next edition of the O’Bayes conference will be in… Warwick on June 29-July 2, as I volunteered to organise this edition (16 years after O’Bayes 03 in Aussois!) just after the BNP meeting in Oxford on June 23-28, hopefully creating the environment for fruitful interactions between both communities! (And jumping from Au’Bayes to Wa’Bayes.)

Filed under: Statistics, Travel, University life Tagged: ABC, Austin, BNP12, canoe, Hyvärinen score, misspecified model, NIPS 2017, O'Ba, O'Bayes 2019, O-Bayes 2017, objective Bayes, safe Bayes, Sardinia, Texas, The University of Texas at Austin, University of Oxford, University of Warwick, Wikiprevia ]]>

Filed under: pictures, Statistics, Travel, University life Tagged: Austin, conference, group picture, ISBA, O'Bayes17, objective Bayes, Texas, The University of Texas at Austin, USA ]]>

Since this approach is most naturally associated with an MCMC implementation, it requires new simulations of the summary statistics at each iteration, without a clear possibility to involve parallel runs, in contrast to ABC. However in the final example of the paper, the authors reach values of n of several thousands, making use of multiple cores relevant, if requiring synchronicity and checks at every MCMC iteration.

The authors mention that “ABC can be viewed as a pseudo-marginal method”, but this has a limited appeal since the pseudo-marginal is a Monte Carlo substitute for the ABC target, not the original target. Similarly, there exists an unbiased estimator of the Gaussian density due to Ghurye and Olkin (1969) that allows to perceive the estimated synthetic likelihood version as a pseudo-marginal, once again wrt a target that differs from the original one. And the bias reappears under mis-specification, that is when the summary statistics are not normally distributed. It seems difficult to assess this normality or absence thereof in realistic situations.

“However, when the distribution of the summary statistic is highly irregular, the output of BSL cannot be trusted, while ABC represents a robust alternative in such cases.”

To make synthetic likelihood and ABC algorithms compatible, the authors chose a Normal kernel for ABC. Still, the equivalence is imperfect in that the covariance matrix need be chosen in the ABC case and is estimated in the synthetic one. I am also lost to the argument that the synthetic version is more efficient than ABC, in general (page 8). As for the examples, the first one uses a toy Poisson posterior with a single sufficient summary statistic, which is not very representative of complex situations where summary statistics are extremes or discrete. As acknowledged by the authors this is a case when the Normality assumption applies. For an integer support hidden process like the Ricker model, normality vanishes and the outcomes of ANC and synthetic likelihood differ, which makes it difficult to compare the inferential properties of both versions (rather than the acceptance rates), while using a 13-dimension statistic for estimating a 3-dimension parameter is not recommended for ABC, as discussed by Li and Fearnhead (2017). The same issue appears in the realistic cell motility example, with 145 summaries versus two parameters. (In the philogenies studied by DIYABC, the number of summary statistics is about the same but we now advocate a projection to the parameter dimension by the medium of random forests.)

Given the similarity between both approaches, I wonder at a confluence between them, where synthetic likelihood could maybe be used to devise PCA on the summary statistics and facilitate their projection on a space with much smaller dimensions. Or estimating the mean and variance functions in the synthetic likelihood towards producing directly simulations of the summary statistics.

Filed under: Statistics Tagged: ABC, ABC consistency, ABC-MCMC, embarassingly parallel, misspecified model, summary statistics, synthetic likelihood, unbiased estimation ]]>

Filed under: pictures, Running, Travel Tagged: Austin, jatp, road running, sunrise, Texas, Texas Capitol ]]>

(z-v)²-<* π*, log

where z is the game winner and ** θ** is the vector of parameters of the neural network. (Details obviously missing above!) The achievements of this new version are even more impressive than those of the earlier one (which managed to systematically beat top Go players) in that blind exploration of game moves repeated over some five million games produced a much better AI player. With a strategy at times remaining a mystery to Go players.

Incidentally a two-page paper appeared on arXiv today with the title *Demystifying AlphaGo Zero*, by Don, Wu, and Zhou. Which sets AlphaGo Zero as a special generative adversarial network. And invoking Wasserstein distance as solving the convergence of the network. To conclude that “it’s not [sic] surprising that AlphaGo Zero show [sic] a good convergence property”… A most perplexing inclusion in arXiv, I would say.

Filed under: Books, pictures, Statistics, Travel Tagged: DeepMind, Go, Nature, University of Warwick ]]>

Filed under: pictures, Running, Travel, University life Tagged: Austin, Colorado, Colorado river, jatp, road running, sunrise, Texas ]]>

Filed under: Statistics Tagged: Amsterdam, cartoon, English grammar, JASP, statistical software, sticker, Trojan horse, University of Amsterdam, Viktor Breekman ]]>

When looking at the version of the algorithm [Algorithm 2] based on two basic acceptance ABC steps, there are two features I find intriguing: (i) the primary step uses a cheap generator to reject early poor values of the parameter, followed by the second step involving a more expensive and exact generator, but I see no impact of the choice of this cheap generator in the acceptance probability; (ii) this is an SMC algorithm with imposed resampling at each iteration but there is no visible step for creating new weights after the resampling step. In the current presentation, it sounds like the weights do not change from the initial step, except for those turning to zero and the renormalisation transforms. Which makes the (unspecified) stratification of little interest if any. I must therefore miss a point in the implementation!

One puzzling sentence in the appendix is that the resampling algorithm used in the SMC step “ensures that every particle that is alive before resampling is represented in the resampled particles”, which reminds me of an argument [possibly a different one] made already in Sisson, Fan and Tanaka (2007) and that we could not validate in our subsequent paper. For resampling to be correct, a form of multinomial sampling must be implemented, even via variance reduction schemes like stratified or systematic sampling.

Filed under: pictures, Statistics, Travel Tagged: ABC-MCMC, ABC-SMC, Biometrika, delayed acceptance, lazy ABC, sequential Monte Carlo, SMC-ABC, stratified sampling ]]>

## Amber warning of snow

- From: 0810 on Sun 10 December
- To: 1800 on Sun 10 December
Updated 6 hours ago Active

A spell of heavy snow is likely over parts of Wales, the Midlands and parts of Northern and Eastern England on Sunday.

Road, rail and air travel delays are likely, as well as stranding of vehicles and public transport cancellations. There is a good chance that some rural communities could become cut off.This is an update to extend the warning area as far south as Gloucestershire, Wiltshire, Oxfordshire, Buckinghamshire, Hertfordshire and Essex.

Filed under: Statistics Tagged: Austin, England, running, snow, University of Warwick, Warwickshire, weather forecasters ]]>

Filed under: pictures, Statistics, Travel, University life Tagged: Bayesian econometrics, bread, Lorraine, Marseille, Méditerranée, Notre-Dame-de-la-Garde, PhD thesis, Saint-Charles, thesis defence, Université Aix Marseille ]]>