## Archive for Journal of the Royal Statistical Society

## misspecified [but published!]

Posted in Statistics with tags ABC, Approximate Bayesian computation, Journal of the Royal Statistical Society, JRSSB, misspecified model, Series B on April 1, 2020 by xi'an## unbiased MCMC discussed at the RSS tomorrow night

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags AABI, coupling, discussion paper, Journal of the Royal Statistical Society, Markov chain Monte Carlo algorithm, MCMC, Read paper, Royal Statistical Society, Series B, unbiasedness, Université Paris Dauphine, Vancouver on December 10, 2019 by xi'an**T**he paper ‘Unbiased Markov chain Monte Carlo methods with couplings’ by Pierre Jacob et al. will be discussed (or Read) tomorrow at the Royal Statistical Society, 12 Errol Street, London, tomorrow night, Wed 11 December, at 5pm London time. With a pre-discussion session at 3pm, involving Chris Sherlock and Pierre Jacob, and chaired by Ioanna Manolopoulou. While I will alas miss this opportunity, due to my trip to Vancouver over the weekend, it is great that that the young tradition of pre-discussion sessions has been rekindled as it helps put the paper into perspective for a wider audience and thus makes the more formal Read Paper session more profitable. As we discussed the paper in Paris Dauphine with our graduate students a few weeks ago, we will for certain send one or several written discussions to Series B!

## a good start in Series B!

Posted in Books, pictures, Statistics, University life with tags ABC, approximate Bayesian inference, generative model, Journal of the Royal Statistical Society, Olympic National Park, peer review, Series B, sunrise, Wasserstein distance on January 5, 2019 by xi'an**J**ust received the great news for the turn of the year that our paper on ABC using Wasserstein distance was accepted in Series B! Inference in generative models using the Wasserstein distance, written by Espen Bernton, Pierre Jacob, Mathieu Gerber, and myself, bypasses the (nasty) selection of summary statistics in ABC by considering the Wasserstein distance between observed and simulated samples. It focuses in particular on non-iid cases like time series in what I find fairly innovative ways. I am thus very glad the paper is going to appear in JRSS B, as it has methodological consequences that should appeal to the community at large.

## selected parameters from observations

Posted in Books, Statistics with tags censored data, FDR, joint dis, Journal of the Royal Statistical Society, random effects, ranking and selection, Stephen Senn, truncated normal on December 7, 2018 by xi'an**I** recently read a fairly interesting paper by Daniel Yekutieli on a Bayesian perspective for parameters selected after viewing the data, published in Series B in 2012. (Disclaimer: I was not involved in processing this paper!)

The first example is to differentiate the Normal-Normal mean posterior when θ is N(0,1) and x is N(θ,1) from the restricted posterior when θ is N(0,1) and x is N(θ,1) truncated to (0,∞). By restating the later as the repeated generation from the joint until x>0. This does not sound particularly controversial, except for the notion of *selecting the parameter after viewing the data*. That the posterior support may depend on the data is not that surprising..!

“The observation that selection affects Bayesian inference carries the important implicationthat in Bayesian analysis of large data sets, for each potential parameter,it is necessary to explicitly specify a selection rule that determines when inferenceis provided for the parameter and provide inference that is based on theselection-adjusted posterior distribution of the parameter.” (p.31)

The more interesting distinction is between “fixed” and “random” parameters (Section 2.1), which separate cases where the data is from a truncated distribution (given the parameter) and cases where the joint distribution is truncated but misses the normalising constant (function of θ) for the truncated sampling distribution. The “mixed” case introduces an hyperparameter λ and the normalising constant integrates out θ and depends on λ. Which amounts to switching to another (marginal) prior on θ. This is quite interesting even though one can debate of the very notions of “random” and “mixed” “parameters”, which are those where the posterior most often changes, as true parameters. Take for instance Stephen Senn’s example (p.6) of the mean associated with the largest observation in a Normal mean sample, with distinct means. When accounting for the distribution of the largest variate, this random variable is no longer a Normal variate with a single unknown mean but it instead depends on all the means of the sample. Speaking of the largest observation mean is therefore misleading in that it is neither the mean of the largest observation, nor a parameter *per se* since the index [of the largest observation] is a random variable induced by the observed sample.

In conclusion, a very original article, if difficult to assess as it can be argued that selection models other than the “random” case result from an intentional modelling choice of the joint distribution.