**O**ur survey paper on “computing Bayes“, written with my friends Gael Martin [who led this project most efficiently!] and David Frazier, has now been revised and resubmitted, the new version being now available on arXiv. Recognising that the entire range of the literature cannot be encompassed within a single review, esp. wrt the theoretical advances made on MCMC, the revised version is more focussed on the approximative solutions (when considering MCMC as “exact”!). As put by one of the referees [which were all very supportive of the paper], *“the authors are very brave. To cover in a review paper the computational methods for Bayesian inference is indeed a monumental task and in a way an hopeless one”*. This is the opportunity to congratulate Gael on her election to the Academy of Social Sciences of Australia last month. (Along with her colleague from Monash, Rob Hyndman.)

## Archive for Monash University

## computing Bayes 2.0

Posted in Books, Statistics, University life with tags Approximate Bayesian computation, arXiv, ASSA, Australia, Bayesian computing, MCMC, Monash University, Monte Carlo methods, Monte Carlo Statistical Methods, review, revision, survey on December 11, 2020 by xi'an## David Frazier’s talk on One World ABC seminar tomorrow [watch for the time!]

Posted in pictures, Statistics, Travel, University life with tags ABC, Australia, Bayesian robustness, daylight saving time, Melbourne, Monash University, One World ABC Seminar, University of Warwick, Victoria, webinar on October 14, 2020 by xi'an**M**y friend and coauthor from Melbourne is giving the One World ABC seminar tomorrow. He will be talking at 10:30 UK time, 11:30 Brussels time, and 20:30 Melbourne time! On Robust and Efficient Approximate Bayesian Computation: A Minimum Distance Approach. Be on time!

## focused Bayesian prediction

Posted in Books, pictures, Statistics, Travel, University life with tags Australia, Bayesian non-parametrics, Bayesian predictive, Casa Matemática Oaxaca, econometrics, likelihood-free inference, Mexico, misspecification, Monash University, One World ABC Seminar, prediction, pseudo-marginal MCMC, score function, webinar on June 3, 2020 by xi'an**I**n this fourth session of our One World ABC Seminar, my friend and coauthor Gael Martin, gave an after-dinner talk on focused Bayesian prediction, more in the spirit of Bissiri et al. than following a traditional ABC approach. because along with Ruben Loaiza-Maya and [my friend and coauthor] David Frazier, they consider the possibility of a (mild?) misspecification of the model. Using thus scoring rules à la Gneiting and Raftery. Gael had in fact presented an earlier version at our workshop in Oaxaca, in November 2018. As in other solutions of that kind, difficulty in weighting the score into a distribution. Although asymptotic irrelevance, direct impact on the current predictions, at least for the early dates in the time series… Further calibration of the set of interest A. Or the focus of the prediction. As a side note the talk perfectly fits the One World likelihood-free seminar as it does not use the likelihood function!

“The very premise of this paper is that, in reality, any choice of predictive class is such that the truth is not contained therein, at which point there is no reason to presume that the expectation of any particular scoring rule will be maximized at the truth or, indeed, maximized by the same predictive distribution that maximizes a different (expected) score.”

This approach requires the proxy class to be close enough to the true data generating model. Or in the word of the authors to be *plausible predictive* models. And to produce the true distribution via the score as it is proper. Or the closest to the true model in the misspecified family. I thus wonder at a possible extension with a non-parametric version, the prior being thus on functionals rather than parameters, if I understand properly the meaning of Π(P_{θ}). (Could the score function be misspecified itself?!) Since the score is replaced with its empirical version, the implementation is resorting to off-the-shelf MCMC. (I wonder for a few seconds if the approach could be seen as a pseudo-marginal MCMC but the estimation is always based on the same observed sample, hence does not directly fit the pseudo-marginal MCMC framework.)

*[Notice: Next talk in the series is tomorrow, 11:30am GMT+1.]*

## stratified ABC [One World ABC webinar]

Posted in Books, Statistics, University life with tags Ascension, Australia, BayesComp 2020, bootstrap likelihood, Gainesville, groundhog day, Monash University, One World ABC Seminar, stratified sampling on May 15, 2020 by xi'an**T**he third episode of the One World ABC seminar (Season 1!) was kindly delivered by Umberto Picchini on Stratified sampling and bootstrapping for ABC which I already if briefly discussed after BayesComp 2020. Which sounds like a million years ago… His introduction on the importance of estimating the likelihood using a kernel, while 600% justified wrt his talk, made the One World ABC seminar sounds almost like groundhog day! The central argument is in the computational gain brought by simulating a single θ dependent [expensive] dataset followed by [cheaper] bootstrap replicates. Which turns de fact into bootstrapping the summary statistics.

If I understand correctly, the post-stratification approach of Art Owen (2013?, I cannot find the reference) corrects a misrepresentation of mine. Indeed, defining a partition with unknown probability weights seemed to me to annihilate the appeal of stratification, because the Bernoulli variance of the estimated probabilities brought back the same variability as the mother estimator. But with bootstrap, this requires only two simulations, one for the weights and one for the target. And further allows for a larger ABC tolerance *in fine*. Free lunch?!

The speaker in two weeks (21 May or Ascension Thursday!) is my friend and co-author Gael Martin from Monash University, who will speak on Focused Bayesian prediction, at quite a late time down under..!

## Computing Bayes: Bayesian Computation from 1763 to the 21st Century

Posted in Books, pictures, Statistics, Travel, University life with tags 1763, Australia, Bayes on the Beach, Bayesian computation, Monash University, survey, Thomas Bayes on April 16, 2020 by xi'an**L**ast night, Gael Martin, David Frazier (from Monash U) and myself arXived a survey on the history of Bayesian computations. This project started when Gael presented a historical overview of Bayesian computation, then entitled ‘Computing Bayes: Bayesian Computation from 1763 to 2017!’, at ‘Bayes on the Beach’ (Queensland, November, 2017). She then decided to build a survey from the material she had gathered, with her usual dedication and stamina. Asking David and I to join forces and bring additional perspectives on this history. While this is a short and hence necessary incomplete history (of not everything!), it hopefully brings some different threads together in an original enough fashion (as I think there is little overlap with recent surveys I wrote). We welcome comments about aspects we missed, skipped or misrepresented, most obviously!