distortion estimates for approximate Bayesian inference

A few days ago, Hanwen Xing, Geoff Nichols and Jeong Eun Lee arXived a paper with the following title, to be presented at uai2020. Towards assessing the fit of the approximation for the actual posterior, given the available data. This covers of course ABC methods (which seems to be the primary focus of the paper) but also variational inference and synthetic likelihood versions. For a parameter of interest, the difference between exact and approximate marginal posterior distributions is see as a distortion map, D = F o G⁻¹, interpreted as in optimal transport and estimated by normalising flows. Even when the approximate distribution G is poorly estimated since D remains the cdf of G(X) when X is distributed from F. The marginal posterior approximate cdf G can be estimated by ABC or another approximate technique. The distortion function D is itself restricted to be a Beta cdf, with parameters estimated by a neural network (although based on which input is unclear to me, unless the weights in (5) are the neural weights). The assessment is based on the estimated distortion at the dataset, as a significant difference from the identity signal a poor fit for the approximation. Overall, the procedure seems implementable rather easily and while depending on calibrating choices (other than the number of layers in the neural network) a realistic version of the simulation-based diagnostic of Talts et al. (2018).

BFF⁷ postponed

Statistics versus Data Science [or not]

Last week a colleague from Warwick forwarded us a short argumentation by Donald Macnaughton (a “Toronto-based statistician”) about switching the name of our field from Statistics to Data Science. This is not the first time I hear of this proposal and this is not the first time I express my strong disagreement with it! Here are the naughtonian arguments

1. Statistics is (at least in the English language) endowed with several meanings from the compilation of numbers out of a series of observations to the field, to the procedures proposed by the field. This is argued to be confusing for laypeople. And missing the connection with data at the core of our field. As well as the indication that statistics gathers information from the data. Data science seems to convey both ideas… But it is equally vague in that most scientific fields if not all rely on data and observations and the structure exploitation of such data. Actually a lot of so-called “data-scientists” have specialised in the analysis of data from their original field, without voluntarily embarking upon a career of data-scientist. And not necessarily acquiring the proper tools for incorporating uncertainty quantification (aka statistics!).
2. Statistics sounds old-fashioned and “old-guard” and “inward-looking” and unattractive to young talents, while they flock to Data Science programs. Which is true [that they flock] but does not mean we [as a field] must flock there as well. In five or ten years, who can tell this attraction of data science(s) will still be that strong. We already had to switch our Master names to Data Science or the like, this is surely more than enough.
3. Data science is encompassing other areas of science, like computer science and operation research, but this is not an issue both in terms of potential collaborations and gaining the upper ground as a “key part” in the field. Which is more wishful thinking than a certainty, given the existing difficulties in being recognised as a major actor in data analysis. (As for instance in a recent grant evaluation in “Big Data” where the evaluation committee involved no statistician. And where we got rejected.)

snapshot from Toronto [guest picture]

a maths mansion!

I read in The Guardian today about James Stewart’s house being for sale. James Stewart was a prolific author of many college and high-school books on calculus and pre-calculus. I have trouble understanding how one can write so many books on the same topic, but he apparently managed, to the point of having this immense house designed by architects to his taste. Which sounds a bit passé in my opinion. Judging from the covers of the books, and from the shape of the house, he had a fascination for the integral sign (which has indeed an intrinsic beauty!). Still amazing considering it was paid by his royalties. Less amazing when checking the price of those books: they are about $250 a piece. Multiplied by hundreds of thousands of copies sold every year, it sums up to being able to afford such a maths mansion! (I am not so sure I can take over the undergrad market by recycling the Bayesian Choice..!)