a journal of the plaid [shirt] year [#2]

Read Kawabata’s Sound of the Mountain, which I also found in a Montréal bookstore. At first, I thought it was connected to the masterpiece House of Sleeping Beauties,  which I read eons ago, as dreams are also central to that (mostly) domestic and familial story, but this was quite another, more personal, and poignant reflection on aging and the irreversibility of time. As well as an unsuspected window into immediate post-war Japan. (With the realisation that abortion was completely acceptable then.) Also spotted Greg Bear’s Darwin’s Children in my Canadian cabin, which I started and finished later with a Kindle version. As I was unaware of a sequel to the fabulous Darwin’s Radio. Overall, I was almost as enthusiastic about it as I was with the first book, but obviously suffering from an academic bias as the author engages into speculative population genetics, which may prove too much for non-academics… (Imho, the end is wasted, though.) And (binge) read January Fifteenth on the flight back (leaving too early to sleep!), which is a short novel whose only speculative aspect is the move (by the US Government) to a universal basic income (UBI) for all individuals, and the consequences on several women’s live. This was indeed a very quick read, presumably due to the high proportion of dialogues, with (variably) interesting characters that avoid a direct take on the concept, but somewhat charicaturesque nonetheless. The implementation of the scheme is rather vaguely described: January 15 is the calendar day people pick their yearly UBI and they have to do it in person to avoid been coerced or scammed into transferring it to someone else. As someone rather interested in this societal propsal, this book did not modify my views on the concept or on its practical aspects, but shed light on some potential consequences of (one version of) it.

Had a great time in a Lac-Saint-Jean cabin, with direct access to the lake. Albeit requiring the emergency purchase of a neoprene swimming suit, as the temperature of the lake was rather low for extended swimming without it. But otherwise, having a swell time every morning, often running and swimming and biking. Before hiking. (The last week, farther south, next to a much smaller lake I could easily cross, did not require the suit!) Also appreciated very much the almost flat véliroute des Bleuets (blueberries) that run all around the lake (even though some sections are alas shared with cars). Has for instance an uninterrupted 15K connection to the nearest (genuine) bakery+cheese-mongery! Made an attempt at kouign amann, but using the wrong type of both flour and cassonade, plus an unknown oven and the poor substitute of baking soda for yeast predictably failed the experiment, even though the outcome was eatable (and eaten within a few days).

As usual (!), did not spot much wildlife, beyond groundhogs, pikas, squirrels, beavers and muskrats in our rental’s lake, moose tracks here and there, and a few Virginia deer in the Mauricie National Park. (Which made me realise that national and regional [Québec] parks co-existed in the area.) Had a few traditional hikes, reconnecting with Deet to keep mosquitoes and black flies at bay.

Watched nothing at all! In part due to my wife often borrowing my laptop for its Netflix connection, in part due to my early sleep caused by earlier rise, as light comes before 5am in this part of Québec we were staying, which made an ideal opportunity for very early run, swim, and… Biometrika editing!

Naturally amazed at non-identifiability

A Nature paper by Stilianos Louca and Matthew W. Pennell,  Extant time trees are consistent with a myriad of diversification histories, comes to the extraordinary conclusion that birth-&-death evolutionary models cannot distinguish between several scenarios given the available data! Namely, stem ages and daughter lineage ages cannot identify the speciation rate function λ(.), the extinction rate function μ(.)  and the sampling fraction ρ inherently defining the deterministic ODE leading to the number of species predicted at any point τ in time, N(τ). The Nature paper does not seem to make a point beyond the obvious and I am rather perplexed at why it got published [and even highlighted]. A while ago, under the leadership of Steve, PNAS decided to include statistician reviewers for papers relying on statistical arguments. It could time for Nature to move there as well.

“We thus conclude that two birth-death models are congruent if and only if they have the same r_p and the same λ_p at some time point in the present or past.” [S.1.1, p.4]

Or, stated otherwise, that a tree structured dataset made of branch lengths are not enough to identify two functions that parameterise the model. The likelihood looks like

$

where E(.) is the probability to survive to the present and ψ(s,t) the probability to survive and be sampled between times s and t. Sort of. Both functions depending on functions λ(.) and  μ(.). (When the stem age is unknown, the likelihood changes a wee bit, but with no changes in the qualitative conclusions. Another way to write this likelihood is in term of the speciation rate λ_p

where Λ_p is the integrated rate, but which shares the same characteristic of being unable to identify the functions λ(.) and μ(.). While this sounds quite obvious the paper (or rather the supplementary material) goes into fairly extensive mode, including “abstract” algebra to define congruence.

 

“…we explain why model selection methods based on parsimony or “Occam’s razor”, such as the Akaike Information Criterion and the Bayesian Information Criterion that penalize excessive parameters, generally cannot resolve the identifiability issue…” [S.2, p15]

As illustrated by the above quote, the supplementary material also includes a section about statistical model selections techniques failing to capture the issue, section that seems superfluous or even absurd once the fact that the likelihood is constant across a congruence class has been stated.

Monte Carlo Markov chains

Darren Wraith pointed out this (currently free access) Springer book by Massimiliano Bonamente [whose family name means good spirit in Italian] to me for its use of the unusual Monte Carlo Markov chain rendering of MCMC.  (Google Trend seems to restrict its use to California!) This is a graduate text for physicists, but one could nonetheless expect more rigour in the processing of the topics. Particularly of the Bayesian topics. Here is a pot-pourri of memorable quotes:

“Two major avenues are available for the assignment of probabilities. One is based on the repetition of the experiments a large number of times under the same conditions, and goes under the name of the frequentist or classical method. The other is based on a more theoretical knowledge of the experiment, but without the experimental requirement, and is referred to as the Bayesian approach.”

“The Bayesian probability is assigned based on a quantitative understanding of the nature of the experiment, and in accord with the Kolmogorov axioms. It is sometimes referred to as empirical probability, in recognition of the fact that sometimes the probability of an event is assigned based upon a practical knowledge of the experiment, although without the classical requirement of repeating the experiment for a large number of times. This method is named after the Rev. Thomas Bayes, who pioneered the development of the theory of probability.”

“The likelihood P(B/A) represents the probability of making the measurement B given that the model A is a correct description of the experiment.”

“…a uniform distribution is normally the logical assumption in the absence of other information.”

“The Gaussian distribution can be considered as a special case of the binomial, when the number of tries is sufficiently large.”

“This clearly does not mean that the Poisson distribution has no variance—in that case, it would not be a random variable!”

“The method of moments therefore returns unbiased estimates for the mean and variance of every distribution in the case of a large number of measurements.”

“The great advantage of the Gibbs sampler is the fact that the acceptance is 100 %, since there is no rejection of candidates for the Markov chain, unlike the case of the Metropolis–Hastings algorithm.”

Let me then point out (or just whine about!) the book using “statistical independence” for plain independence, the use of / rather than Jeffreys’ | for conditioning (and sometimes forgetting \ in some LaTeX formulas), the confusion between events and random variables, esp. when computing the posterior distribution, between models and parameter values, the reliance on discrete probability for continuous settings, as in the Markov chain chapter, confusing density and probability, using Mendel’s pea data without mentioning the unlikely fit to the expected values (or, as put more subtly by Fisher (1936), “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel’s expectations”), presenting Fisher’s and Anderson’s Iris data [a motive for rejection when George was JASA editor!] as a “a new classic experiment”, mentioning Pearson but not Lee for the data in the 1903 Biometrika paper “On the laws of inheritance in man” (and woman!), and not accounting for the discrete nature of this data in the linear regression chapter, the three page derivation of the Gaussian distribution from a Taylor expansion of the Binomial pmf obtained by differentiating in the integer argument, spending endless pages on deriving standard properties of classical distributions, this appalling mess of adding over the conditioning atoms with no normalisation in a Poisson experiment

,

botching the proof of the CLT, which is treated before the Law of Large Numbers, restricting maximum likelihood estimation to the Gaussian and Poisson cases and muddling its meaning by discussing unbiasedness, confusing a drifted Poisson random variable with a drift on its parameter, as well as using the pmf of the Poisson to define an area under the curve (Fig. 5.2), sweeping the improperty of a constant prior under the carpet, defining a null hypothesis as a range of values for a summary statistic, no mention of Bayesian perspectives in the hypothesis testing, model comparison, and regression chapters, having one-dimensional case chapters followed by two-dimensional case chapters, reducing model comparison to the use of the Kolmogorov-Smirnov test, processing bootstrap and jackknife in the Monte Carlo chapter without a mention of importance sampling, stating recurrence results without assuming irreducibility, motivating MCMC by the intractability of the evidence, resorting to the term link to designate the current value of a Markov chain, incorporating the need for a prior distribution in a terrible description of the Metropolis-Hastings algorithm, including a discrete proof for its stationarity, spending many pages on early 1990’s MCMC convergence tests rather than discussing the adaptive scaling of proposal distributions, the inclusion of numerical tables [in a 2017 book] and turning Bayes (1763) into Bayes and Price (1763), or Student (1908) into Gosset (1908).

[Usual disclaimer about potential self-plagiarism: this post or an edited version of it could possibly appear later in my Books Review section in CHANCE. Unlikely, though!]

another mirror of ABC in Gre[e]noble

There will now be a second mirror workshop of ABC in Grenoble. Taking place at the Université de Montpellier, more precisely at the Alexander Grothendieck Montpellier Institute, Building 9, room 430 (4th floor), Triolet Campus. It is organised by my friend Jean-Michel Marin. Great to see a mirror at one of the major breeding places of ABC, where I personally heard of ABC for the first time and met several of the main A[B]Ctors..! The dates are 19-20 March, with talks transmitted from 9am to 5am [GMT+1]. Since the video connection can accommodate 1918 more mirrors, if anyone else is interested in organising another mirror, please contact me for technical details.

down with Galton (and Pearson and Fisher…)

In the last issue of Significance, which I read in Warwick prior to the conference, there is a most interesting article on Galton’s eugenics, his heritage at University College London (UCL), and the overall trouble with honouring prominent figures of the past with memorials like named building or lectures… The starting point of this debate is a protest from some UCL students and faculty about UCL having a lecture room named after the late Francis Galton who was a professor there. Who further donated at his death most of his fortune to the university towards creating a professorship in eugenics. The protests are about Galton’s involvement in the eugenics movement of the late 18th and early 19th century. As well as professing racist opinions.

My first reaction after reading about these protests was why not?! Named places or lectures, as well as statues and other memorials, have a limited utility, especially when the named person is long dead and they certainly do not contribute in making a scientific theory [associated with the said individual] more appealing or more valid. And since “humans are [only] humans”, to quote Stephen Stigler speaking in this article, it is unrealistic to expect great scientists to be perfect, the more if one multiplies the codes for ethical or acceptable behaviours across ages and cultures. It is also more rational to use amphitheater MS.02 and lecture room AC.18 rather than associate them with one name chosen out of many alumni’s or former professors’.

Predictably, another reaction of mine was why bother?!, as removing Galton’s name from the items it is attached to is highly unlikely to change current views on eugenism or racism. On the opposite, it seems to detract from opposing the present versions of these ideologies. As some recent proposals linking genes and some form of academic success. Another of my (multiple) reactions was that as stated in the article these views of Galton’s reflected upon the views and prejudices of the time, when the notions of races and inequalities between races (as well as genders and social classes) were almost universally accepted, including in scientific publications like the proceedings of the Royal Society and Nature. When Karl Pearson launched the Annals of Eugenics in 1925 (after he started Biometrika) with the very purpose of establishing a scientific basis for eugenics. (An editorship that Ronald Fisher would later take over, along with his views on the differences between races, believing that “human groups differ profoundly in their innate capacity for intellectual and emotional development”.) Starting from these prejudiced views, Galton set up a scientific and statistical approach to support them, by accumulating data and possibly modifying some of these views. But without much empathy for the consequences, as shown in this terrible quote I found when looking for more material:

“I should feel but little compassion if I saw all the Damaras in the hand of a slave-owner, for they could hardly become more wretched than they are now…”

As it happens, my first exposure to Galton was in my first probability course at ENSAE when a terrific professor was peppering his lectures with historical anecdotes and used to mention Galton’s data-gathering trip to Namibia, literally measure local inhabitants towards his physiognomical views , also reflected in the above attempt of his to superpose photographs to achieve the “ideal” thief…