## Bayes Rules! [book review]

Posted in Books, Kids, Mountains, pictures, R, Running, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on July 5, 2022 by xi'an

Bayes Rules! is a new introductory textbook on Applied Bayesian Model(l)ing, written by Alicia Johnson (Macalester College), Miles Ott (Johnson & Johnson), and Mine Dogucu (University of California Irvine). Textbook sent to me by CRC Press for review. It is available (free) online as a website and has a github site, as well as a bayesrule R package. (Which reminds me that both our own book R packages, bayess and mcsm, have gone obsolete on CRAN! And that I should find time to figure out the issue for an upgrading…)

As far as I can tell [from abroad and from only teaching students with a math background], Bayes Rules! seems to be catering to early (US) undergraduate students with very little exposure to mathematical statistics or probability, as it introduces basic probability notions like pmf, joint distribution, and Bayes’ theorem (as well as Greek letters!) and shies away from integration or algebra (a covariance matrix occurs on page 437 with a lot . For instance, the Normal-Normal conjugacy derivation is considered a “mouthful” (page 113). The exposition is somewhat stretched along the 500⁺ pages as a result, imho, which is presumably a feature shared with most textbooks at this level, and, accordingly, the exercises and quizzes are more about intuition and reproducing the contents of the chapter than technical. In fact, I did not spot there a mention of sufficiency, consistency, posterior concentration (almost made on page 113), improper priors, ergodicity, irreducibility, &tc., while other notions are not precisely defined, like ESS, weakly informative (page 234) or vague priors (page 77), prior information—which makes the negative answer to the quiz “All priors are informative”  (page 90) rather confusing—, R-hat, density plot, scaled likelihood, and more.

As an alternative to “technical derivations” Bayes Rules! centres on intuition and simulation (yay!) via its bayesrule R package. Itself relying on rstan. Learning from example (as R code is always provided), the book proceeds through conjugate priors, MCMC (Metropolis-Hasting) methods, regression models, and hierarchical regression models. Quite impressive given the limited prerequisites set by the authors. (I appreciated the representations of the prior-likelihood-posterior, especially in the sequential case.)

Regarding the “hot tip” (page 108) that the posterior mean always stands between the prior mean and the data mean, this should be made conditional on a conjugate setting and a mean parameterisation. Defining MCMC as a method that produces a sequence of realisations that are not from the target makes a point, except of course that there are settings where the realisations are from the target, for instance after a renewal event. Tuning MCMC should remain a partial mystery to readers after reading Chapter 7 as the Goldilocks principle is quite vague. Similarly, the derivation of the hyperparameters in a novel setting (not covered by the book) should prove a challenge, even though the readers are encouraged to “go forth and do some Bayes things” (page 509).

While Bayes factors are supported for some hypothesis testing (with no point null), model comparison follows more exploratory methods like X validation and expected log-predictive comparison.

The examples and exercises are diverse (if mostly US centric), modern (including cultural references that completely escape me), and often reflect on the authors’ societal concerns. In particular, their concern about a fair use of the inferred models is preminent, even though a quantitative assessment of the degree of fairness would require a much more advanced perspective than the book allows… (In that respect, Exercise 18.2 and the following ones are about book banning (in the US). Given the progressive tone of the book, and the recent ban of math textbooks in the US, I wonder if some conservative boards would consider banning it!) Concerning the Himalaya submitting running example (Chapters 18 & 19), where the probability to summit is conditional on the age of the climber and the use of additional oxygen, I am somewhat surprised that the altitude of the targeted peak is not included as a covariate. For instance, Ama Dablam (6848 m) is compared with Annapurna I (8091 m), which has the highest fatality-to-summit ratio (38%) of all. This should matter more than age: the Aosta guide Abele Blanc climbed Annapurna without oxygen at age 57! More to the point, the (practical) detailed examples do not bring unexpected conclusions, as for instance the fact that runners [thrice alas!] tend to slow down with age.

A geographical comment: Uluru (page 267) is not a city!, but an impressive sandstone monolith in the heart of Australia, a 5 hours drive away from Alice Springs. And historical mentions: Alan Turing (page 10) and the team at Bletchley Park indeed used Bayes factors (and sequential analysis) in cracking the Enigma, but this remained classified information for quite a while. Arianna Rosenbluth (page 10, but missing on page 165) was indeed a major contributor to Metropolis et al.  (1953, not cited), but would not qualify as a Bayesian statistician as the goal of their algorithm was a characterisation of the Boltzman (or Gibbs) distribution, not statistical inference. And David Blackwell’s (page 10) Basic Statistics is possibly the earliest instance of an introductory Bayesian and decision-theory textbook, but it never mentions Bayes or Bayesianism.

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Book Review section in CHANCE.]

## Alain Turing cash!

Posted in pictures, Travel with tags , , , , , , , , , , , on April 8, 2021 by xi'an

## Suffrage Science awards in maths and computing

Posted in pictures, Statistics, University life with tags , , , , , , , , , , , on October 21, 2016 by xi'an

On October 11, at Bletchley Park, the Suffrage Science awards in mathematics and computer sciences were awarded for the first time to 12 senior female researchers. Among whom three statisticians, Professor Christl Donnelly from Imperial College London, my colleague at Warwick, Jane Hutton, and my friend and co-author, Sylvia Richardson, from MRC, Cambridge University. This initiative was started by the Medical Research Council in 2011 by Suffrage Science awards for life sciences, followed in 2013 by one for engineering and physics, and this year for maths and computing. The name of the award aims to connect with the Suffragette movement of the late 19th and early 20th Centuries, which were particularly active in Britain. One peculiar aspect of this award is that the recipients are given pieces of jewellery, created for each field, pieces that they will themselves give two years later to a new recipient of their choice, and so on in an infinite regress! (Which suggests a related puzzle, namely to figure out how many years it should take until all female scientists have received the award. But since the number increases as the square of the number of years, this is not going to happen unless the field proves particularly hostile to women scientists!) This jewellery award also relates to the history of the Suffragette movement since the WPSU commissioned their own jewellery awards. A clever additional touch was that the awards were delivered on Ada Lovelace Day, October 11.

## a Simpson paradox of sorts

Posted in Books, Kids, pictures, R with tags , , , , , , , , , on May 6, 2016 by xi'an

The riddle from The Riddler this week is about finding an undirected graph with N nodes and no isolated node such that the number of nodes with more connections than the average of their neighbours is maximal. A representation of a connected graph is through a matrix X of zeros and ones, on which one can spot the nodes satisfying the above condition as the positive entries of the vector (X1)^2-(X^21), if 1 denotes the vector of ones. I thus wrote an R code aiming at optimising this target

```targe <- function(F){
sum(F%*%F%*%rep(1,N)/(F%*%rep(1,N))^2<1)}
```

by mere simulated annealing:

```rate <- function(N){
# generate matrix F
# 1. no single
F=matrix(0,N,N)
F[sample(2:N,1),1]=1
F[1,]=F[,1]
for (i in 2:(N-1)){
if (sum(F[,i])==0)
F[sample((i+1):N,1),i]=1
F[i,]=F[,i]}
if (sum(F[,N])==0)
F[sample(1:(N-1),1),N]=1
F[N,]=F[,N]
# 2. more connections
F[lower.tri(F)]=F[lower.tri(F)]+
sample(0:1,N*(N-1)/2,rep=TRUE,prob=c(N,1))
F[F>1]=1
F[upper.tri(F)]=t(F)[upper.tri(t(F))]
#simulated annealing
T=1e4
temp=N
targo=targe(F)
for (t in 1:T){
#1. local proposal
nod=sample(1:N,2)
prop=F
prop[nod[1],nod[2]]=prop[nod[2],nod[1]]=
1-prop[nod[1],nod[2]]
while (min(prop%*%rep(1,N))==0){
nod=sample(1:N,2)
prop=F
prop[nod[1],nod[2]]=prop[nod[2],nod[1]]=
1-prop[nod[1],nod[2]]}
target=targe(prop)
if (log(runif(1))*temp<target-targo){
F=prop;targo=target}
#2. global proposal
prop=F prop[lower.tri(prop)]=F[lower.tri(prop)]+
sample(c(0,1),N*(N-1)/2,rep=TRUE,prob=c(N,1))
prop[prop>1]=1
prop[upper.tri(prop)]=t(prop)[upper.tri(t(prop))]
target=targe(prop)
if (log(runif(1))*temp<target-targo){
F=prop;targo=target}
temp=temp*.999
}
return(F)}
```

This code returns quite consistently (modulo the simulated annealing uncertainty, which grows with N) the answer N-2 as the number of entries above average! Which is rather surprising in a Simpson-like manner since all entries but two are above average. (Incidentally, I found out that Edward Simpson recently wrote a paper in Significance about the Simpson-Yule paradox and him being a member of the Bletchley Park Enigma team. I must have missed out the connection with the Simpson paradox when reading the paper in the first place…)

## Turing’s Bayesian contributions

Posted in Books, Kids, pictures, Running, Statistics, University life with tags , , , , , , , , , , , , on March 17, 2015 by xi'an

Following The Imitation Game, this recent movie about Alan Turing played by Benedict “Sherlock” Cumberbatch, been aired in French theatres, one of my colleagues in Dauphine asked me about the Bayesian contributions of Turing. I first tried to check in Sharon McGrayne‘s book, but realised it had vanished from my bookshelves, presumably lent to someone a while ago. (Please return it at your earliest convenience!) So I told him about the Bayesian principle of updating priors with data and prior probabilities with likelihood evidence in code detecting algorithms and ultimately machines at Bletchley Park… I could not got much farther than that and hence went checking on Internet for more fodder.

“Turing was one of the independent inventors of sequential analysis for which he naturally made use of the logarithm of the Bayes factor.” (p.393)

I came upon a few interesting entries but the most amazìng one was a 1979 note by I.J. Good (assistant of Turing during the War) published in Biometrika retracing the contributions of Alan Mathison Turing during the War. From those few pages, it emerges that Turing’s statistical ideas revolved around the Bayes factor that Turing used “without the qualification `Bayes’.” (p.393) He also introduced the notion of ban as a unit for the weight of evidence, in connection with the town of Banbury (UK) where specially formatted sheets of papers were printed “for carrying out an important classified process called Banburismus” (p.394). Which shows that even in 1979, Good did not dare to get into the details of Turing’s work during the War… And explains why he was testing simple statistical hypothesis against simple statistical hypothesis. Good also credits Turing for the expected weight of evidence, which is another name for the Kullback-Leibler divergence and for Shannon’s information, whom Turing would visit in the U.S. after the War. In the final sections of the note, Turing is also associated with Gini’s index, the estimation of the number of species (processed by Good from Turing’s suggestion in a 1953 Biometrika paper, that is, prior to Turing’s suicide. In fact, Good states in this paper that “a very large part of the credit for the present paper should be given to [Turing]”, p.237), and empirical Bayes.