**J**ust received an email today that our discussion with Judith of Chris Holmes and James Watson’s paper was now published as *Statistical Science 2016, Vol. 31, No. 4, 506-510*… While it is almost identical to the arXiv version, it can be read on-line.

## Archive for Conan Doyle

## nonparametric Bayesian clay for robust decision bricks

Posted in Statistics with tags Bayesian robustness, Chris Holmes, Conan Doyle, discussion paper, James Watson, Judith Rousseau, Statistical Science on January 30, 2017 by xi'an## comments on Watson and Holmes

Posted in Books, pictures, Statistics, Travel with tags Bayesian Analysis, Bayesian robustness, Conan Doyle, decision theory, Dirichlet process, Kullback-Leibler divergence, Saint Giles cemetery, Sherlock Holmes, Statistical Science, University of Oxford on April 1, 2016 by xi'an

“The world is full of obvious things which nobody by any chance ever observes.” The Hound of the Baskervilles

**I**n connection with the incoming publication of James Watson’s and Chris Holmes’ Approximating models and robust decisions in Statistical Science, Judith Rousseau and I wrote a discussion on the paper that has been arXived yesterday.

“Overall, we consider that the calibration of the Kullback-Leibler divergence remains an open problem.” (p.18)

While the paper connects with earlier ones by Chris and coauthors, and possibly *despite* the overall critical tone of the comments!, I really appreciate the renewed interest in robustness advocated in this paper. I was going to write *Bayesian robustness* but to differ from the perspective adopted in the 90’s where robustness was mostly about the prior, I would say this is rather a Bayesian approach to model robustness from a decisional perspective. With definitive innovations like considering the impact of posterior uncertainty over the decision space, uncertainty being defined e.g. in terms of Kullback-Leibler neighbourhoods. Or with a Dirichlet process distribution on the posterior. This may step out of the standard Bayesian approach but it remains of definite interest! (And note that this discussion of ours [reluctantly!] refrained from capitalising on the names of the authors to build easy puns linked with the most Bayesian of all detectives!)

## Sherlock [#3]

Posted in Books with tags amazon associates, BBC, Bristol, Conan Doyle, Goldney Hall, Sherlock Holmes, TV series on March 14, 2015 by xi'an**A**fter watching the first two seasons of the BBC TV Series Sherlock while at the hospital, I found myself looking forward further adventures of Holmes and Watson and eventually “bought” the third season. And watched it over the past weekends. I liked it very much as this new season distanced itself from the sheer depiction of Sherlock’s amazing powers to a quite ironic and self-parodic story, well in tune with a third season where the audience is now utterly familiar with the main characters. They all put on weight (mostly figuratively!), from Sherlock’s acknowledgement of his psychological shortcomings, to Mrs. Hudson’s revealing her drug trafficking past and expressing her dislike of Mycroft, to John Watson’s engagement and acceptance of Sherlock’s idiosyncrasies, making him the central character of the series in a sort of fatherly figure. Some new characters are also terrific, including Mary Morstan and the new archvillain, C.A. Magnussen. Paradoxically, this makes the detective part of the stories secondary, which is all for the best as, in my opinion, the plots are rather weak and the resolutions hardly relying on high intellectual powers, albeit always surprising. More sleuthing in the new season would be most welcome! As an aside, the wedding place sounded somewhat familiar to me, until I realised it was Goldney Hall, where the recent workshops I attended in Bristol took place.

## Unusual timing shows how random mass murder can be (or even less)

Posted in Books, R, Statistics, Travel with tags birthday problem, coincidence, Conan Doyle, mass murders, Pittsburgh, Richard von Mises, The Sign of Four, Toronto, USA Today on November 29, 2013 by xi'an**T**his post follows the original one on the headline of the USA Today I read during my flight to Toronto last month. I remind you that the unusual pattern was about observing four U.S. mass murders happening within four days, “for the first time in at least seven years”. Which means that the difference between the four dates is at most 3, not 4!

**I** asked my friend Anirban Das Gupta from Purdue University are the exact value of this probability and the first thing he pointed out was that I used a different meaning of “within 4”. He then went into an elaborate calculation to find an upper bound on this probability, upper bound that was way above my Monte Carlo approximation and my rough calculation of last post. I rechecked my R code and found it was not achieving the right approximation since one date was within 3 days of three other days, at least… I thus rewrote the following R code

T=10^6 four=rep(0,T) for (t in 1:T){ day=sort(sample(1:365,30,rep=TRUE)) #30 random days day=c(day,day[day>363]-365) #account for toric difference tem=outer(day,day,"-") four[t]=(max(apply(((tem>-1)&(tem<4)),1,sum)>3)) } mean(four)

*[checked it was ok for two dates within 1 day, resulting in the birthday problem probability]* and found 0.070214, which is much larger than the earlier value and shows it takes an average 14 years for the “unlikely” event to happen! And the chances that it happens within seven years is 40%.

**A**nother coincidence relates to this evaluation, namely the fact that two elderly couples in France committed couple suicide within three days, last week. I however could not find the figures for the number of couple suicides per year. Maybe because it is extremely rare. Or undetected…

## Unusual timing shows how random mass murder can be (or not)

Posted in Books, R, Statistics, Travel with tags birthday problem, coincidence, Conan Doyle, mass murders, Pittsburgh, Richard von Mises, The Sign of Four, Toronto, USA Today on November 4, 2013 by xi'an**T**his was one headline in the USA Today I picked from the hotel lobby on my way to Pittsburgh airport and then Toronto this morning. The unusual pattern was about observing four U.S. mass murders happening within four days, “for the first time in at least seven years”. The article did not explain why this was unusual. And reported one mass murder expert’s opinion instead of a statistician’s…

**N**ow, there are about 30 mass murders in the U.S. each year (!), so the probability of finding at least four of those 30 events within 4 days of one another should be related to von Mises‘ birthday problem. For instance, Abramson and Moser derived in 1970 that the probability that at least two people (among n) have birthday within k days of one another (for an m days year) is

but I did not find an extension to the case of the four (to borrow from Conan Doyle!)… A quick approximation would be to turn the problem into a birthday problem with 364/4=91 days and count the probability that four share the same birthday

which is surprisingly large. So I checked with a R code in the plane:

T=10^5 four=rep(0,T) for (t in 1:T){ day=sample(1:365,30,rep=TRUE) four[t]=(max(apply((abs(outer(day,day,"-"))<4),1,sum))>4)} mean(four)

and found 0.0278, which means the above approximation is far from terrible! I think it may actually be “exact” in the sense that observing *exactly* four murders within four days of one another is given by this probability. The cases of five, six, &tc. murders are omitted but they are also highly negligible. And from this number, we can see that there is a 18% probability that the case of the four occurs within seven years. Not so unlikely, then.