## ABC & the eighth plague of Egypt [locusts in forests]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on April 6, 2021 by xi'an

“If you refuse to let them go, I will bring locusts into your country tomorrow. They will cover the face of the ground so that it cannot be seen. They will devour what little you have left after the hail, including every tree that is growing in your fields. They will fill your houses and those of all your officials and all the Egyptians.” Exodus 10:3-6

Marie-Pierre Chapuis, Louis Raynal, and co-authors, mostly from Montpellier, published last year a paper on the evolutionary history of the African arid-adapted pest locust, Schistocerca gregaria, called the eighth plague of Egypt in the Bible. And a cause for a major food disaster in East Africa over the past months. The analysis was run with ABC-RF techniques. The paper was first reviewed in PCI Evolutionary Biology, with the following points:

The present-day distribution of extant species is the result of the interplay between their past population demography (e.g., expansion, contraction, isolation, and migration) and adaptation to the environment (…) The understanding of the key factors driving species evolution gives important insights into how the species may respond to changing conditions, which can be particularly relevant for the management of harmful species, such as agricultural pests.

Meaningful demographic inferences present major challenges. These include formulating evolutionary scenarios fitting species biology and the eco-geographical context and choosing informative molecular markers and accurate quantitative approaches to statistically compare multiple demographic scenarios and estimate the parameters of interest. A further issue comes with result interpretation. Accurately dating the inferred events is far from straightforward since reliable calibration points are necessary to translate the molecular estimates of the evolutionary time into absolute time units (i.e. years). This can be attempted in different ways (…) Nonetheless, most experimental systems rarely meet these conditions, hindering the comprehensive interpretation of results.

The contribution of Chapuis et al. addresses these issues to investigate the recent history of the (…) desert locust (…) Owing to their fast mutation rate microsatellite markers offer at least two advantages: i) suitability for analyzing recently diverged populations, and ii) direct estimate of the germline mutation rate in pedigree samples (…) The main aim of the study is to infer the history of divergence of the two subspecies of the desert locust, which have spatially disjoint distribution corresponding to the dry regions of North and West-South Africa. They first use paleo-vegetation maps to formulate hypotheses about changes in species range since the last glacial maximum. Based on them, they generate 12 divergence models. For the selection of the demographic model and parameter estimation, they apply the recently developed ABC-RF approach (…) Some methodological novelties are also introduced in this work, such as the computation of the error associated with the posterior parameter estimates under the best scenario (…) The best-supported model suggests a recent divergence event of the subspecies of S. gregaria (around 2.6 kya) and a reduction of populations size in one of the subspecies (S. g. flaviventris) that colonized the southern distribution area. As such, results did not support the hypothesis that the southward colonization was driven by the expansion of African dry environments associated with the last glacial maximum (…) The estimated time of divergence points at a much more recent origin for the two subspecies, during the late Holocene, in a period corresponding to fairly stable arid conditions similar to current ones. Although the authors cannot exclude that their microsatellite data bear limited information on older colonization events than the last one, they bring arguments in favour of alternative explanations. The hypothesis privileged does not involve climatic drivers, but the particularly efficient dispersal behaviour of the species, whose individuals are able to fly over long distances (up to thousands of kilometers) under favourable windy conditions (…)

There is a growing number of studies in phylogeography in arid regions in the Southern hemisphere, but the impact of past climate changes on the species distribution in this region remains understudied relative to the Northern hemisphere. The study presented by Chapuis et al. offers several important insights into demographic changes and the evolutionary history of an agriculturally important pest species in Africa, which could also mirror the history of other organisms in the continent (…)

Microsatellite markers have been offering a useful tool in population genetics and phylogeography for decades (…) This study reaffirms the usefulness of these classic molecular markers to estimate past demographic events, especially when species- and locus-specific microsatellite mutation features are available and a powerful inferential approach is adopted. Nonetheless, there are still hurdles to overcome, such as the limitations in scenario choice associated with the simulation software used (e.g. not allowing for continuous gene flow in this particular case), which calls for further improvement of simulation tools allowing for more flexible modeling of demographic events and mutation patterns. In sum, this work not only contributes to our understanding of the makeup of the African biodiversity but also offers a useful statistical framework, which can be applied to a wide array of species and molecular markers.

## down with Galton (and Pearson and Fisher…)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , on July 22, 2019 by xi'an

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…

## A precursor of ABC-Gibbs

Posted in Books, R, Statistics with tags , , , , , , , , , , on June 7, 2019 by xi'an

All ABC algorithms, including ABC-PaSS introduced here, require that statistics are sufficient for estimating the parameters of a given model. As mentioned above, parameter-wise sufficient statistics as required by ABC-PaSS are trivial to find for distributions of the exponential family. Since many population genetics models do not follow such distributions, sufficient statistics are known for the most simple models only. For more realistic models involving multiple populations or population size changes, only approximately-sufficient statistics can be found.

While Gibbs sampling is not mentioned in the paper, this is indeed a form of ABC-Gibbs, with the advantage of not facing convergence issues thanks to the sufficiency. The drawback being that this setting is restricted to exponential families and hence difficult to extrapolate to non-exponential distributions, as using almost-sufficient (or not) summary statistics leads to incompatible conditionals and thus jeopardise the convergence of the sampler. When thinking a wee bit more about the case treated by Kousathanas et al., I am actually uncertain about the validation of the sampler. When tolerance is equal to zero, this is not an issue as it reproduces the regular Gibbs sampler. Otherwise, each conditional ABC step amounts to introducing an auxiliary variable represented by the simulated summary statistic. Since the distribution of this summary statistic depends on more than the parameter for which it is sufficient, in general, it should also appear in the conditional distribution of other parameters. At least from this Gibbs perspective, it thus relies on incompatible conditionals, which makes the conditions proposed in our own paper the more relevant.

## contemporary issues in hypothesis testing

Posted in Statistics with tags , , , , , , , , , , , , , , , , , , on September 26, 2016 by xi'an

This week [at Warwick], among other things, I attended the CRiSM workshop on hypothesis testing, giving the same talk as at ISBA last June. There was a most interesting and unusual talk by Nick Chater (from Warwick) about the psychological aspects of hypothesis testing, namely about the unnatural features of an hypothesis in everyday life, i.e., how far this formalism stands from human psychological functioning.  Or what we know about it. And then my Warwick colleague Tom Nichols explained how his recent work on permutation tests for fMRIs, published in PNAS, testing hypotheses on what should be null if real data and getting a high rate of false positives, got the medical imaging community all up in arms due to over-simplified reports in the media questioning the validity of 15 years of research on fMRI and the related 40,000 papers! For instance, some of the headings questioned the entire research in the area. Or transformed a software bug missing the boundary effects into a major flaw.  (See this podcast on Not So Standard Deviations for a thoughtful discussion on the issue.) One conclusion of this story is to be wary of assertions when submitting a hot story to journals with a substantial non-scientific readership! The afternoon talks were equally exciting, with Andrew explaining to us live from New York why he hates hypothesis testing and prefers model building. With the birthday model as an example. And David Draper gave an encompassing talk about the distinctions between inference and decision, proposing a Jaynes information criterion and illustrating it on Mendel‘s historical [and massaged!] pea dataset. The next morning, Jim Berger gave an overview on the frequentist properties of the Bayes factor, with in particular a novel [to me] upper bound on the Bayes factor associated with a p-value (Sellke, Bayarri and Berger, 2001)

B¹⁰(p) ≤ 1/-e p log p

with the specificity that B¹⁰(p) is not testing the original hypothesis [problem] but a substitute where the null is the hypothesis that p is uniformly distributed, versus a non-parametric alternative that p is more concentrated near zero. This reminded me of our PNAS paper on the impact of summary statistics upon Bayes factors. And of some forgotten reference studying Bayesian inference based solely on the p-value… It is too bad I had to rush back to Paris, as this made me miss the last talks of this fantastic workshop centred on maybe the most important aspect of statistics!

## a general framework for updating belief functions

Posted in Books, Statistics, University life with tags , , , , , , , , , on July 15, 2013 by xi'an

Pier Giovanni Bissiri, Chris Holmes and Stephen Walker have recently arXived the paper related to Sephen’s talk in London for Bayes 250. When I heard the talk (of which some slides are included below), my interest was aroused by the facts that (a) the approach they investigated could start from a statistics, rather than from a full model, with obvious implications for ABC, & (b) the starting point could be the dual to the prior x likelihood pair, namely the loss function. I thus read the paper with this in mind. (And rather quickly, which may mean I skipped important aspects. For instance, I did not get into Section 4 to any depth. Disclaimer: I wasn’t nor is a referee for this paper!)

The core idea is to stick to a Bayesian (hardcore?) line when missing the full model, i.e. the likelihood of the data, but wishing to infer about a well-defined parameter like the median of the observations. This parameter is model-free in that some degree of prior information is available in the form of a prior distribution. (This is thus the dual of frequentist inference: instead of a likelihood w/o a prior, they have a prior w/o a likelihood!) The approach in the paper is to define a “posterior” by using a functional type of loss function that balances fidelity to prior and fidelity to data. The prior part (of the loss) ends up with a Kullback-Leibler loss, while the data part (of the loss) is an expected loss wrt to l(THETASoEUR,x), ending up with the definition of a “posterior” that is

$\exp\{ -l(\theta,x)\} \pi(\theta)$

the loss thus playing the role of the log-likelihood.

I like very much the problematic developed in the paper, as I think it is connected with the real world and the complex modelling issues we face nowadays. I also like the insistence on coherence like the updating principle when switching former posterior for new prior (a point sorely missed in this book!) The distinction between M-closed M-open, and M-free scenarios is worth mentioning, if only as an entry to the Bayesian processing of pseudo-likelihood and proxy models. I am however not entirely convinced by the solution presented therein, in that it involves a rather large degree of arbitrariness. In other words, while I agree on using the loss function as a pivot for defining the pseudo-posterior, I am reluctant to put the same faith in the loss as in the log-likelihood (maybe a frequentist atavistic gene somewhere…) In particular, I think some of the choices are either hard or impossible to make and remain unprincipled (despite a call to the LP on page 7).  I also consider the M-open case as remaining unsolved as finding a convergent assessment about the pseudo-true parameter brings little information about the real parameter and the lack of fit of the superimposed model. Given my great expectations, I ended up being disappointed by the M-free case: there is no optimal choice for the substitute to the loss function that sounds very much like a pseudo-likelihood (or log thereof). (I thought the talk was more conclusive about this, I presumably missed a slide there!) Another great expectation was to read about the proper scaling of the loss function (since L and wL are difficult to separate, except for monetary losses). The authors propose a “correct” scaling based on balancing both faithfulness for a single observation, but this is not a completely tight argument (dependence on parametrisation and prior, notion of a single observation, &tc.)

The illustration section contains two examples, one of which is a full-size or at least challenging  genetic data analysis. The loss function is based on a logistic  pseudo-likelihood and it provides results where the Bayes factor is in agreement with a likelihood ratio test using Cox’ proportional hazard model. The issue about keeping the baseline function as unkown reminded me of the Robbins-Wasserman paradox Jamie discussed in Varanasi. The second example offers a nice feature of putting uncertainties onto box-plots, although I cannot trust very much the 95%  of the credibles sets. (And I do not understand why a unique loss would come to be associated with the median parameter, see p.25.)

Watch out: Tomorrow’s post contains a reply from the authors!