## continuous herded Gibbs sampling

Posted in Books, pictures, Statistics with tags , , , , , , , , on June 28, 2021 by xi'an

Read a short paper by Laura Wolf and Marcus Baum on Gibbs herding, where herding is a technique of “deterministic sampling”, for instance selecting points over the support of the distribution by matching exact and empirical (or “empirical”!) moments. Which reminds me of the principal points devised by my late friend Bernhard Flury. With an unclear argument as to why it could take over random sampling:

“random numbers are often generated by pseudo-random number generators, hence are not truly random”

Especially since the aim is to “draw samples from continuous multivariate probability densities.” The sequential construction of such a sample proceeds sequentially by adding a new (T+1)-th point to the existing sample of y’s by maximising in x the discrepancy

$(T+1)\mathbb E^Y[k(x,Y)]-\sum_{t=1}^T k(x,y_t)$

where k(·,·) is a kernel, e.g. a Gaussian density. Hence a complexity that grows as O(T). The current paper suggests using Gibbs “sampling” to update one component of x at a time. Using the conditional version of the above discrepancy. Making the complexity grow as O(dT) in d dimensions.

I remain puzzled by the whole thing as these samples cannot be used as regular random or quasi-random samples. And in particular do not produce unbiased estimators of anything. Obviously. The production of such samples being furthermore computationally costly it is also unclear to me that they could even be used for quick & dirty approximations of a target sample.

## a new Monty Hall riddle

Posted in Books, Kids, Mountains, pictures, R, Statistics, Travel with tags , , , , , , , , , on May 22, 2020 by xi'an

The Riddler was sort of feeling the rising boredom of being under lockdown when proposing the following variant to the Monty Hall puzzle:

There are zero to three goats, with a probability ¼ each, and they are allocated to different doors uniformly among the three doors of the show. After the player chooses a door, Monty opens another door hidding a goat or signals this is impossible. Given that he did open a door, what is the probability that the player’s door does not hide a goat?

Indeed, a straightforward conditional probability computation considering all eight possible cases with the four cases corresponding to Monty opening a door leads to a probability of 3/8 for the player’s door. As confirmed by the following R code:

s=sample
m=c(0,0)
for(t in 1:1e6)m=m+(range(s(1:3,s(1:3,1)))>1)


## strange loyalties [book review]

Posted in Statistics with tags , , , , , , , , , , , on April 26, 2020 by xi'an

This book by William McIlvarnney is the third and last one in the Laidlaw investigation series and the most original of the three as far as I am concerned… For it is more an inner quest than a crime investigation, as the detective is seeking an explanation to the accidental death of his brother as well as the progressive deterioration of their relation, while trying to make sense of his own life and his relation to women. It is thus as far a crime novel as it is possible, although there are criminals involved. And Laidlaw cannot separate his “job” from his personal life, meaning he does investigate on his free time the death of his brother.  It is entirely written in a first-person perspective, which makes the reading harder and slower in my case. But an apt conclusion to the trilogy, rather than being pulled into finer and finer threads as other detective stories. Brilliant (like the light on Skye during the rain).

“Life was only in the living of it. How you act and what you are and what you do and how you be were the only substance. They didn’t last either. But while you were here, they made what light there was – the wick that threads the candle-grease of time. His light was out but here I felt I could almost smell the smoke still drifting from its snuffing.”

## Bayesian econometrics in St. Andrews

Posted in Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , on April 8, 2019 by xi'an
A call I received for the incoming 2019 edition of the European Seminar on Bayesian Econometrics (ESOBE), sponsored by the EFaB section of ISBA, which is going to be held at the University of St Andrews in Scotland on Monday 2 and Tuesday 3 September, 2019. I have attended an earlier edition in Venezia and enjoyed it very much. Plus, summer in Scotland…, where else?! Submission of papers is still open:
We aim to have a balance of keynotes from both statistics and econometrics, in order to stimulate submissions from statisticians working on Bayesian methodology or applications in economics/finance. We particularly welcome submissions from young Bayesians (PhDs, PostDocs, assistant professors — EFaB funds a “young researcher session” with up to \$500 per speaker).

## blood hunt [book review]

Posted in Books, University life with tags , , , , , , , , , , on October 28, 2018 by xi'an

I realised just lately that I had not read the early non-Rebus novels of Ian Rankin (written as Jack Harvey) and thus ordered cheap used copies of three of these, which waited for me on my (new) desk when I returned to Warwick. The first one I tried is Blood Hunt, a 1995 conspiracy novel that is so full of clichés that it feels like several volumes long..! I almost left it in the common room before heading back to Paris! To wit, a second-rate journalist is after a big international chemical corporation that is poisoning the entire planet. As he gets too close to exposing the truth, he is assassinated in the US. Fortunately, his brother is a super-hero, an ex SAS soldier, living on one of the Outer Hebrides in massive isolation and getting a living [while remaining very fit] by training “weekend soldiers”. If this sounds like too much of a coincidence, the story gets downhill from there and the suspension of belief gets so heavy that one could walk on it all the way from Uist to Skye! With the main character achieving on his own more than a dozen Jason Bourne, despite a horde of killers set after him. The only thing of interest in the book is how old it sounds, being set before 1995, with hardly any cell phone available and money running out of call cards. The action taking place in France is rather well documented, including a visit to Orly airport, except for the unfortunate mention that entries are found both left and right on the Périphérique! It is fortunate that Rankin chose to adopt a highly different perspective on a similar character when writing Knots & Crosses and creating Rebus, as I would not have possibly continued reading this type of books! And be waiting for getting my hands on the novel House of Lies, which I saw in the airport when leaving.