# Author: xi'an

## Le Monde puzzle [#1085]

A new Le Monde mathematical puzzle in the digit category: Given 13 arbitrary relative integers chosen by Bo, Abigail can select any subset of them to be drifted by plus or minus one by Bo, repeatedly until Abigail reaches the largest possible number N of multiples of 5. What is the minimal possible value of […]

## take a random integer

A weird puzzle from FiveThirtyEight: what is the probability that the product of three random integers is a multiple of 100? Ehrrrr…, what is a random integer?! The solution provided by the Riddler is quite stunning Reading the question charitably (since “random integer” has no specific meaning), there will be an answer if there is […]

## say cheese [jatp]

A picture taken at Jericho Cheese, Little Clarendon Street, Oxford, that I took this week when I visited this cheesemonger for the first time, after several years of passing by its tantalizing display of British cheeses! It happens to have become my most popular picture on Instagram, ranking above the fiery sunrise over the Calanques, […]

## undecidable learnability

“There is an unknown probability distribution P over some finite subset of the interval [0,1]. We get to see m i.i.d. samples from P for m of our choice. We then need to find a finite subset of [0,1] whose P-measure is at least 2/3. The theorem says that the standard axioms of mathematics cannot […]

## O’Bayes 19: registration and travel support

An update about the O’Bayes 19 conference next June-July:  the early registration period has now opened. And there should be funds for supporting early-career researchers, thanks to Google and CNRS sponsorships, as detailed below: Early-career researchers less than four years from PhD, are invited to apply for early-career scholarships. If you are a graduate student, […]

## I’m getting the point

A long-winded X validated discussion on the [textbook] mean-variance conjugate posterior for the Normal model left me [mildly] depressed at the point and use of answering questions on this forum. Especially as it came at the same time as a catastrophic outcome for my mathematical statistics exam.  Possibly an incentive to quit X validated as […]

## I’m getting the point

A long-winded X validated discussion on the [textbook] mean-variance conjugate posterior for the Normal model left me [mildly] depressed at the point and use of answering questions on this forum. Especially as it came at the same time as a catastrophic outcome for my mathematical statistics exam.  Possibly an incentive to quit X validated as […]

## a pen for ABC

Among the flury of papers arXived around the ICML 2019 deadline, I read on my way back from Oxford a paper by Wiqvist et al. on learning summary statistics for ABC by neural nets. Pointing out at another recent paper by Jiang et al. (2017, Statistica Sinica) which constructed a neural network for predicting each […]

## scalable Metropolis-Hastings

Among the flury of arXived papers of last week (414!), including a fair chunk of papers submitted to ICML 2019, I spotted one entry by Cornish et al. on scalable Metropolis-Hastings, which Arnaud Doucet had mentioned to me yesterday when in Oxford. The paper builds on the delayed acceptance paper we wrote with Marco Banterlé, […]

## Fisher’s lost information

After a post on X validated and a good discussion at work, I came to the conclusion [after many years of sweeping the puzzle under the carpet] that the (a?) Fisher information obtained for the Uniform distribution U(0,θ) as θ⁻¹ is meaningless. Indeed, there are many arguments: The lack of derivability of the indicator function […]

## Fate & Fortune [book review]

After enjoying very much the first book, Hue & Cry, in the Hew Cullan series by Shirley McKay, I bought the following ones and read Fate & Fortune over the vacation break. If anything, I enjoyed this one even more, as it disclosed other aspects of 16th Century Scotland, still with the oppressive domination of […]

## Jeffreys priors for hypothesis testing [Bayesian reads #2]

A second (re)visit to a reference paper I gave to my OxWaSP students for the last round of this CDT joint program. Indeed, this may be my first complete read of Susie Bayarri and Gonzalo Garcia-Donato 2008 Series B paper, inspired by Jeffreys’, Zellner’s and Siow’s proposals in the Normal case. (Disclaimer: I was not […]

## airport static

[An annoyingly loud businessman negotiating a deal for hours in Birmingham airport] …you are left with this money and you get the 60, we get 107 is the mathematics…if we discount 40% Werner still gets that, it’s not well-presented, you should get that minus that, do you mind if we do it from scratch, call […]

As a reading suggestion for my (last) OxWaSP Bayesian course at Oxford, I included the classic 1973 Marginalisation paradoxes by Phil Dawid, Mervyn Stone [whom I met when visiting UCL in 1992 since he was sharing an office with my friend Costas Goutis], and Jim Zidek. Paper that also appears in my (recent) slides as […]

## Le Monde puzzle [#1083]

A Le Monde mathematical puzzle that seems hard to solve without the backup of a computer (and just simple enough to code on a flight to Montpellier): Given the number N=2,019, find a decomposition of N as a sum of non-trivial powers of integers such that (a) the number of integers in the sum is […]

## information maximising neural networks summaries

After missing the blood moon eclipse last night, I had a meeting today at the Paris observatory (IAP), where we discussed an ABC proposal made by Tom Charnock, Guilhem Lavaux, and Benjamin Wandelt from this institute. “We introduce a simulation-based machine learning technique that trains artificial neural networks to find non-linear functionals of data that […]

## the paper where you are a node

Sophie Donnet pointed out to me this arXived paper by Tianxi Li, Elizaveta Levina, and Ji Zhu, on a network resampling strategy for X validation, where I appear as a datapoint rather than as a [direct] citation! Which reminded me of the “where you are the hero” gamebooks with which my kids briefly played, before […]