**V**eronicka Rockova (from Chicago Booth) gave a talk on this theme at the Oxford Stats seminar this afternoon. Starting with a survey of ABC, synthetic likelihoods, and pseudo-marginals, to motivate her approach via GANs, learning an approximation of the likelihood from the GAN discriminator. Her explanation for the GAN type estimate was crystal clear and made me wonder at the connection with Geyer’s 1994 logistic estimator of the likelihood (a form of discriminator with a fixed generator). She also expressed the ABC approximation hence created as the actual posterior times an exponential tilt. Which she proved is of order 1/n. And that a random variant of the algorithm (where the shift is averaged) is unbiased. Most interestingly requiring no calibration and no tolerance. Except indirectly when building the discriminator. And no summary statistic. Noteworthy tension between correct shape and correct location.

## Archive for ABC consistency

## Metropolis-Hastings via classification

Posted in pictures, Statistics, Travel, University life with tags ABC, ABC consistency, Chicago, Chicago Booth School of Business, deep learning, discriminant analysis, GANs, logistic regression, seminar, summary statistics, synthetic likelihood, University of Oxford, webinar, winter running on February 23, 2021 by xi'an## ABC forecasts

Posted in Books, pictures, Statistics with tags ABC, ABC consistency, Australia, forecasting, MCMC convergence, Monash University, prediction, state space model, time series on January 9, 2018 by xi'an**M**y friends and co-authors David Frazier, Gael Martin, Brendan McCabe, and Worapree Maneesoonthorn arXived a paper on ABC forecasting at the turn of the year. ABC prediction is a natural extension of ABC inference in that, provided the full conditional of a future observation given past data and parameters is available but the posterior is not, ABC simulations of the parameters induce an approximation of the predictive. The paper thus considers the impact of this extension on the precision of the predictions. And argues that it is possible that this approximation is preferable to running MCMC in some settings. A first interesting result is that using ABC and hence conditioning on an insufficient summary statistic has no asymptotic impact on the resulting prediction, provided Bayesian concentration of the corresponding posterior takes place as in our convergence paper under revision.

“…conditioning inference about θ on η(y) rather than y makes no difference to the probabilistic statements made about [future observations]”

The above result holds both in terms of convergence in total variation and for proper scoring rules. Even though there is always a loss in accuracy in using ABC. Now, one may think this is a direct consequence of our (and others) earlier convergence results, but numerical experiments on standard time series show the distinct feature that, while the [MCMC] posterior and ABC posterior distributions on the parameters clearly differ, the predictives are more or less identical! With a potential speed gain in using ABC, although comparing parallel ABC versus non-parallel MCMC is rather delicate. For instance, a preliminary parallel ABC could be run as a burnin’ step for parallel MCMC, since all chains would then be roughly in the stationary regime. Another interesting outcome of these experiments is a case when the summary statistics produces a non-consistent ABC posterior, but still leads to a very similar predictive, as shown on this graph.This unexpected accuracy in prediction may further be exploited in state space models, towards producing particle algorithms that are greatly accelerated. Of course, an easy objection to this acceleration is that the impact of the approximation is unknown and un-assessed. However, such an acceleration leaves room for multiple implementations, possibly with different sets of summaries, to check for consistency over replicates.

## MCM 2017 snapshots [#2]

Posted in Books, pictures, Running, Statistics, University life with tags ABC, ABC consistency, abcrf, Art Owen, GNU C library, MCM 2017, Mersenne Twisters, Monte Carlo Statistical Methods, Montréal, R, random forests, ratio of uniform algorithm on July 7, 2017 by xi'an**O**n the second day of MCM 2017, Emmanuel Gobet (from Polytechnique) gave the morning plenary talk on regression Monte Carlo methods, where he presented several ways of estimating conditional means of rv’s in nested problems where conditioning involves other conditional expectations. While interested in such problems in connection with ABC, I could not see how the techniques developed therein could apply to said problems.

By some of random chance, I ended up attending a hard-core random generation session where the speakers were discussing discrepancies between GNU library generators [I could not understand the target of interest and using MCMC till convergence seemed prone to false positives!], and failed statistical tests of some 64-bit Mersenne Twisters, and low discrepancy on-line subsamples of Uniform samples. Most exciting of all, Josef Leydold gave a talk on ratio-of-uniforms, on which I spent some time a while ago (till ending up reinventing the wheel!), with highly refined cuts of the original box.

My own 180 slides [for a 50mn talk] somewhat worried my chairman, Art Owen, who kindly enquired the day before at the likelihood I could go through all 184 of them!!! I had appended the ABC convergence slides to an earlier set of slides on ABC with random forests in case of questions about that aspect, although I did not plan to go through those slides [and I mostly covered the 64 other slides] As the talk was in fine more about an inference method than a genuine Monte Carlo technique, plus involved random forests that sounded unfamiliar to many, I did not get many questions from the audience but had several deep discussions with people after the talk. Incidentally, we have just reposted our paper on ABC estimation via random forests, updated the abcrf R package, and submitted it to Peer Community in Evolutionary Biology!