**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!

## Archive for JCGS

## 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## ABC by QMC

Posted in Books, Kids, Statistics, University life with tags ABC, ABC-PMC, ABC-SMC, CREST, JCGS, PhD thesis, population genetics, population Monte Carlo, qMC, quasi-Monte Carlo methods, variance reduction on November 5, 2018 by xi'an**A** paper by Alexander Buchholz (CREST) and Nicolas Chopin (CREST) on quasi-Monte Carlo methods for ABC is going to appear in the *Journal of Computational and Graphical Statistics*. I had missed the opportunity when it was posted on arXiv and only became aware of the paper’s contents when I reviewed Alexander’s thesis for the doctoral school. The fact that the parameters are simulated (in ABC) from a prior that is quite generally a standard distribution while the pseudo-observations are simulated from a complex distribution (associated with the intractability of the likelihood function) means that the use of quasi-Monte Carlo sequences is in general only possible for the first part.

The ABC context studied there is close to the original version of ABC rejection scheme [as opposed to SMC and importance versions], the main difference standing with the use of M pseudo-observations instead of one (of the same size as the initial data). This repeated version has been discussed and abandoned in a strict Monte Carlo framework in favor of M=1 as it increases the overall variance, but the paper uses this version to show that the multiplication of pseudo-observations in a quasi-Monte Carlo framework does not increase the variance of the estimator. (Since the variance apparently remains constant when taking into account the generation time of the pseudo-data, we can however dispute the interest of this multiplication, except to produce a constant variance estimator, for some targets, or to be used for convergence assessment.) L The article also covers the bias correction solution of Lee and Latuszyǹski (2014).

Due to the simultaneous presence of pseudo-random and quasi-random sequences in the approximations, the authors use the notion of mixed sequences, for which they extend a one-dimension central limit theorem. The paper focus on the estimation of Z(ε), the normalization constant of the ABC density, ie the predictive probability of accepting a simulation which can be estimated at a speed of O(N⁻¹) where N is the number of QMC simulations, is a wee bit puzzling as I cannot figure the relevance of this constant (function of ε), especially since the result does not seem to generalize directly to other ABC estimators.

A second half of the paper considers a sequential version of ABC, as in ABC-SMC and ABC-PMC, where the proposal distribution is there based on a Normal mixture with a *small* number of components, estimated from the (particle) sample of the previous iteration. Even though efficient techniques for estimating this mixture are available, this innovative step requires a calculation time that should be taken into account in the comparisons. The construction of a decreasing sequence of tolerances ε seems also pushed beyond and below what a sequential approach like that of Del Moral, Doucet and Jasra (2012) would produce, it seems with the justification to always prefer the lower tolerances. This is not necessarily the case, as recent articles by Li and Fearnhead (2018a, 2018b) and ours have shown (Frazier et al., 2018). Overall, since ABC methods are large consumers of simulation, it is interesting to see how the contribution of QMC sequences results in the reduction of variance and to hope to see appropriate packages added for standard distributions. However, since the most consuming part of the algorithm is due to the simulation of the pseudo-data, in most cases, it would seem that the most relevant focus should be on QMC add-ons on this part, which may be feasible for models with a huge number of standard auxiliary variables as for instance in population evolution.

## 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!

## Gibbs for incompatible kids

Posted in Books, Statistics, University life with tags Bayesian GANs, convergence of Gibbs samplers, GANs, Gibbs for Kids, Gibbs sampling, irreducibility, JCGS, Markov chains, MCMC algorithms, Monte Carlo Statistical Methods, stationarity on September 27, 2018 by xi'an**I**n continuation of my earlier post on Bayesian GANs, which resort to strongly incompatible conditionals, I read a 2015 paper of Chen and Ip that I had missed. (Published in the Journal of Statistical Computation and Simulation which I first confused with JCGS and which I do not know at all. Actually, when looking at its editorial board, I recognised only one name.) But the study therein is quite disappointing and not helping as it considers Markov chains on finite state spaces, meaning that the transition distributions are matrices, meaning also that convergence is ensured if these matrices have no null probability term. And while the paper is motivated by realistic situations where incompatible conditionals can reasonably appear, the paper only produces illustrations on two and three states Markov chains. Not that helpful, in the end… The game is still afoot!

## weakly informative reparameterisations

Posted in Books, pictures, R, Statistics, University life with tags Bayesian modelling, Edinburgh, Gaussian mixture, JCGS, location-scale parameterisation, moments, non-informative priors, publication, R package, Ultimixt on February 14, 2018 by xi'an**O**ur paper, weakly informative reparameterisations of location-scale mixtures, with Kaniav Kamary and Kate Lee, got accepted by JCGS! Great news, which comes in perfect timing for Kaniav as she is currently applying for positions. The paper proposes a unidimensional mixture Bayesian modelling based on the first and second moment constraints, since these turn the remainder of the parameter space into a compact. While we had already developed an associated R package, Ultimixt, the current editorial policy of JCGS imposes the R code used to produce all results to be attached to the submission and it took us a few more weeks than it should have to produce a directly executable code, due to internal library incompatibilities. (For this entry, I was looking for a link to our special JCGS issue with my picture of Edinburgh but realised I did not have this picture.)