capture-recapture rediscovered

A recent Science paper applies capture-recapture to estimating how much medieval literature has been lost, using ancient lists of works and comparing with the currently know corpus. To deduce at a 91% loss. Which begets the next question of how many ancient lists have been lost! Or how many of the observed ones are sheer copies of the others. First I thought I had no access to the paper so could not comment on the specific data and accounting for the uneven and unrandom sampling behind this modelling… But I still would not share the anti-modelling bias of this Harvard historian, given the superlative record of Anne Chao in capture-recapture methodology!

“The paper seems geared more toward systems theorists and statisticians, says Daniel Smail, a historian at Harvard University who studies medieval social and cultural history, and the authors haven’t done enough to establish why cultural production should follow the same rules as life systems. But for him, the bigger question is: Given that we already have catalogs of ancient texts, and previous estimates were pretty close to the model’s new one, what does the new work add?”

Once at Ca’Foscari, I realised the local network gave me access to the paper. The description of the Chao1 method, as far as I can tell, does not describe how the problematic collection of catalogs where duplicates (recaptures) can be observed is taken into account. For one thing, the collection is far from iid since some catalogs must have built on earlier ones. It is also surprising imho that the authors spend space on discussing unbiasedness when a more crucial issue is the randomness assumption behind the collected data.

Measuring abundance [book review]

This 2020 book, Measuring Abundance:  Methods for the Estimation of Population Size and Species Richness was written by Graham Upton, retired professor of applied statistics, for the Data in the Wild series published by Pelagic Publishing, a publishing company based in Exeter.

“Measuring the abundance of individuals and the diversity of species are core components of most ecological research projects and conservation monitoring. This book brings together in one place, for the first time, the methods used to estimate the abundance of individuals in nature.”

Its purpose is to provide a collection of statistical methods for measuring animal abundance or lack thereof. There are four parts: a primer on statistical methods, going no further than maximum likelihood estimation and bootstrap. The term Bayesian only occurs once, in connection with the (a-Bayesian) BIC. (I first spotted a second entry, until I realised this was not a typo and the example truly was about Bawean warty pigs!) The second part is about stationary (or static) individuals, such as trees, and it mostly exposes different recognised ways of sampling, with a focus on minimising the surveyor’s effort. Examples include forestry sampling (with a chainsaw method!) and underwater sampling. There is very little statistics involved in this part apart from the rare appearance of a MLE with an asymptotic confidence interval. There is also very little about misspecified models, except for the occasional warning that the estimates may prove completely wrong. The third part is about mobile individuals, with capture-recapture methods receiving the lion’s share (!). No lion was actually involved in the studies used as examples (but there were grizzly bears from Yellowstone and Banff National Parks). Given the huge variety of capture-recapture models, very little input is found within the book as the practical aspects are delegated to R software like the RMark and mra packages. Very little is written on using covariates or spatial features in such models, mostly dedicated to printed output from R packages with AIC as the sole standard for comparing models. I did not know of distance methods (Chapter 8), which are less invasive counting methods. They however seem to rely on a particular model of missing on individuals as the distance increases. The last section is about estimating the number of species. With again a model assumption that may prove wrong. With the inclusion of diversity measures,

The contents of the book are really down to earth and intended for field data gatherers. For instance, “drive slowly and steadily at 20 mph with headlights and hazard lights on ” (p.91) or “Before starting to record, allow fish time to acclimatize to the presence of divers” (p.91). It is unclear to me how useful the book would prove to be for general statisticians, apart from revealing the huge diversity of methods actually employed in the field. To either build upon these or expose students to their reassessment. More advanced books are McCrea and Morgan (2014), Buckland et al. (2016) and the most recent Seber and Schofield (2019).

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

21w5107 [day 2]

After a rich and local (if freezing) dinner on a rooftop facing the baroque Oaxaca cathedral, and an early invigorating outdoor swim in my case!, the morning session was mostly on mixtures, with Helen Ogden exploring X validation for (estimating the number k of components for) finite mixtures, when using the likelihood as an objective function. I was unclear of the goal however when considering that the data supporting the study was Uniform (0,1), nothing like a mixture of Normal distributions. And about the consistency attached to the objective function. The session ended with Diana Cai presenting a counter-argument in the sense that she proved, along with Trevor Campbell and Tamara Broderick, that the posterior on k diverges to infinity with the number n of observations if a mixture model is misspecified for said data. Which does not come as a major surprise since there is no properly defined value of k when the data is not generated from the adopted mixture. I would love to see an extension to the case when the k component mixture contains a non-parametric component! In-between, Alexander Ly discussed Bayes factors for multiple datasets, with some asymptotics showing consistency for some (improper!) priors if one sample size grows to infinity. With actually attaining the same rate under both hypotheses. Luis Nieto-Barajas presented an approach on uncertainty assessment through KL divergence for random probability measures, which requires a calibration of the KL in this setting, as KL does not enjoy a uniform scale, and a prior on a Pólya tree. And Chris Holmes presented a recent work with Edwin Fong and Steven Walker on a prediction approach to Bayesian inference. Which I had had on my reading list for a while. It is a very original proposal where likelihoods and priors are replaced by the sequence of posterior predictives and only parameters of interest get simulated. The Bayesian flavour of the approach is delicate to assess though, albeit a form of non-parametric Bayesian perspective… (I still need to read the paper carefully.)

In the afternoon session, Judith Rousseau presented her recent foray in cut posteriors for semi-parametric HMMs. With interesting outcomes for efficiently estimating the transition matrix, the component distributions, and the smoothing distribution. I wonder at the connection with safe Bayes in that cut posteriors induce a loss of information. Sinead Williamson spoke on distributed MCMC for BNP. Going back at the “theme of the day”, namely clustering and finding the correct (?) number of clusters. With a collapsed versus uncollapsed division that reminded me of the marginal vs. conditional María Gil-Leyva discussed yesterday. Plus a decomposition of a random measure into a finite mixture and an infinite one that also reminded me of the morning talk of Diana Cai. (And making me wonder at the choice of the number K of terms in the finite part.) Michele Guindani spoke about clustering distributions (with firecrackers as a background!). Using the nDP mixture model, which was show to suffer from degeneracy (as discussed by Frederico Camerlenghi et al. in BA). The subtle difference stands in using the same (common) atoms in all random distributions at the top of the hierarchy, with independent weights. Making the partitions partially exchangeable. The approach relies on Sylvia’s generalised mixtures of finite mixtures. With interesting applications to microbiome and calcium imaging (including a mice brain in action!). And Giovanni Rebaudo presented a generalised notion of clustering aligned on a graph, with some observations located between the nodes corresponding to clusters. Represented as a random measure with common parameters for the clusters and separated parameters outside. Interestingly playing on random partitions, Pólya urns, and species sampling.