Archive for population genetics

ABC by QMC

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , on November 5, 2018 by xi'an

A paper by Alexander Buchholz (CREST) and Nicolas Chopin (CREST) on quasi-Monte Carlo methods for ABC is going to appear in the Journal of Computational and Graphical Statistics. I had missed the opportunity when it was posted on arXiv and only became aware of the paper’s contents when I reviewed Alexander’s thesis for the doctoral school. The fact that the parameters are simulated (in ABC) from a prior that is quite generally a standard distribution while the pseudo-observations are simulated from a complex distribution (associated with the intractability of the likelihood function) means that the use of quasi-Monte Carlo sequences is in general only possible for the first part.

The ABC context studied there is close to the original version of ABC rejection scheme [as opposed to SMC and importance versions], the main difference standing with the use of M pseudo-observations instead of one (of the same size as the initial data). This repeated version has been discussed and abandoned in a strict Monte Carlo framework in favor of M=1 as it increases the overall variance, but the paper uses this version to show that the multiplication of pseudo-observations in a quasi-Monte Carlo framework does not increase the variance of the estimator. (Since the variance apparently remains constant when taking into account the generation time of the pseudo-data, we can however dispute the interest of this multiplication, except to produce a constant variance estimator, for some targets, or to be used for convergence assessment.) L The article also covers the bias correction solution of Lee and Latuszyǹski (2014).

Due to the simultaneous presence of pseudo-random and quasi-random sequences in the approximations, the authors use the notion of mixed sequences, for which they extend a one-dimension central limit theorem. The paper focus on the estimation of Z(ε), the normalization constant of the ABC density, ie the predictive probability of accepting a simulation which can be estimated at a speed of O(N⁻¹) where N is the number of QMC simulations, is a wee bit puzzling as I cannot figure the relevance of this constant (function of ε), especially since the result does not seem to generalize directly to other ABC estimators.

A second half of the paper considers a sequential version of ABC, as in ABC-SMC and ABC-PMC, where the proposal distribution is there  based on a Normal mixture with a small number of components, estimated from the (particle) sample of the previous iteration. Even though efficient techniques for estimating this mixture are available, this innovative step requires a calculation time that should be taken into account in the comparisons. The construction of a decreasing sequence of tolerances ε seems also pushed beyond and below what a sequential approach like that of Del Moral, Doucet and Jasra (2012) would produce, it seems with the justification to always prefer the lower tolerances. This is not necessarily the case, as recent articles by Li and Fearnhead (2018a, 2018b) and ours have shown (Frazier et al., 2018). Overall, since ABC methods are large consumers of simulation, it is interesting to see how the contribution of QMC sequences results in the reduction of variance and to hope to see appropriate packages added for standard distributions. However, since the most consuming part of the algorithm is due to the simulation of the pseudo-data, in most cases, it would seem that the most relevant focus should be on QMC add-ons on this part, which may be feasible for models with a huge number of standard auxiliary variables as for instance in population evolution.

MCM 2017

Posted in Statistics with tags , , , , , , , , , , , , on July 3, 2017 by xi'an

And thus I am back in Montréal, for MCM 2017, located in HEC Montréal, on the campus of Université de Montréal, for three days. My talk is predictably about ABC, what else?!, gathering diverse threads from different talks and papers:

Darwin’s radio [book review]

Posted in Books, Kids, pictures, University life with tags , , , , , , , , , , , , , , , , on September 10, 2016 by xi'an

When in Sacramento two weeks ago I came across the Beers Books Center bookstore, with a large collection of used and (nearly) new cheap books and among other books I bought Greg Bear’s Darwin Radio. I had (rather) enjoyed another book of his’, Hull Zero Three, not to mention one of his first books, Blood Music, I read in the mid 1980’s, and the premises of this novel sounded promising, not mentioning the Nebula award. The theme is of a major biological threat, apparently due to a new virus, and of the scientific unraveling of what the threat really means. (Spoilers alert!) In that respect it sounds rather similar to the (great) Crichton‘s The Andromeda Strain, which is actually mentioned by some characters in this book. As is Ebola, as a sort of contrapoint (since Ebola is a deadly virus, although the epidemic in Western Africa now seems to have vanished). The biological concept exploited here is dormant DNA in non-coding parts of the genome that periodically get awaken and induce massive steps in the evolution. So massive that carriers of those mutations are killed by locals. Until the day it happens in an all-connected World and the mutation can no longer be stopped. The concept is compelling if not completely convincing of course, while the outcome of a new human race, which is to Homo Sapiens what Homo Sapiens was to Neanderthal, is rather disappointing. (How could it be otherwise?!) But I did appreciate the postulate of a massive and immediate change in the genome, even though the details were disputable and the dismissal of Dawkins‘ perspective poorly defended. From a stylistic perspective, the style is at time heavy, while there are too many chance occurrences, like the main character happening to be in Georgia for a business deal (spoilers, spoilers!) at the times of the opening of collective graves, or the second main character coming upon a couple of Neanderthal mummies with a Sapiens baby, or yet this pair of main characters falling in love and delivering a live mutant baby-girl. But I enjoyed reading it between San Francisco and Melbourne, with a few hours of lost sleep and work. It is a page turner, no doubt! I also like the political undercurrents, from riots to emergency measures, to an effective dictatorship controlling pregnancies and detaining newborns and their mothers.

One important thread in the book deals with anthropology digs getting against Native claims to corpses and general opposition to such digs. This reminded me of a very recent article in Nature where a local Indian tribe had claimed rights to several thousand year old skeletons, whose DNA was then showed to be more related with far away groups than the claimants. But where the tribe was still granted the last word, in a rather worrying jurisprudence.

the new version of abcrf

Posted in pictures, R, Statistics, University life with tags , , , , , , on June 7, 2016 by xi'an

gaarden tree, Jan. 16, 2012A new version of the R package abcrf has been posted on Friday by Jean-Michel Marin, in conjunction with the recent arXival of our paper on point estimation via ABC and random forests. The new R functions come to supplement the existing ones towards implementing ABC point estimation:

  1. covRegAbcrf, which predicts the posterior covariance between those two response variables, given a new dataset of summaries.
  2. plot.regAbcrf, which provides a variable importance plot;
  3. predict.regabcrf, which predicts the posterior expectation, median, variance, quantiles for a given parameter and a new dataset;
  4. regAbcrf, which produces a regression random forest from a reference table aimed out predicting posterior expectation, variance and quantiles for a parameter;
  5. snp, a simulated example in population genetics used as reference table in our Bioinformatics paper.

Unfortunately, we could not produce directly a diyabc2abcrf function for translating a regular DIYABC output into a proper abcrf format, since the translation has to occur in DIYABC instead. And even this is not a straightforward move (to be corrected in the next version of DIYABC).

postdoc on Bayesian computation for statistical genomics

Posted in Kids, Statistics, Travel, University life with tags , , , , , on February 24, 2016 by xi'an

[An opportunity to work with Richard Everitt in Reading, UK, in a postdoc position starting this summer]

It is now possible to retrieve the complete DNA sequence of a bacterial strain relatively quickly and cheaply, and population genetics has been revolutionised in the past ten years through the availability of these data. To gain a deep understanding of sequence data, model-based statistical techniques are required. However, current approaches for performing inference in these models do not scale to whole genome sequence data. The BBSRC project “Understanding recombination through tractable statistical analysis of whole genome sequences” aims to address this issue. A position as Post-Doctoral Research Assistant is available on this project, supervised by Dr Richard Everitt in the Statistics group at the Department of Mathematics & Statistics at the University of Reading.

The deadline for applications is March 31, 2016 (details).

JSM 2015 [day #3]

Posted in Books, Statistics, University life with tags , , , , , , , , , , on August 12, 2015 by xi'an

My first morning session was about inference for philogenies. While I was expecting some developments around Kingman’s  coalescent models my coauthors needed and developped ABC for, I was surprised to see models that were producing closed form (or close enough to) likelihoods. Due to strong restrictions on the population sizes and migration possibilities, as explained later to me by Vladimir Minin. No need for ABC there since MCMC was working on the species trees, with Vladimir Minin making use of [the Savage Award winner] Vinayak Rao’s approach on trees that differ from the coalescent. And enough structure to even consider and demonstrate tree identifiability in Laura Kubatko’s case.

I then stopped by the astrostatistics session as the first talk by Gwendolin Eddie was about galaxy mass estimation, a problem I may actually be working on in the Fall, but it ended up being a completely different problem and I was further surprised that the issue of whether or not the data was missing at random was not considered by the authors.searise3

Christening a session Unifying foundation(s) may be calling for trouble, at least from me! In this spirit, Xiao Li Meng gave a talk attempting at a sort of unification of the frequentist, Bayesian, and fiducial paradigms by introducing the notion of personalized inference, which is a notion I had vaguely thought of in the past. How much or how far do you condition upon? However, I have never thought of this justifying fiducial inference in any way and Xiao Li’s lively arguments during and after the session not enough to convince me of the opposite: Prior-free does not translate into (arbitrary) choice-free. In the earlier talk about confidence distributions by Regina Liu and Minge Xie, that I partly missed for Galactic reasons, I just entered into the room at the very time when ABC was briefly described as a confidence distribution because it was not producing a convergent approximation to the exact posterior, a logic that escapes me (unless those confidence distributions are described in such a loose way as to include about any method f inference). Dongchu Sun also gave us a crash course on reference priors, with a notion of random posteriors I had not heard of before… As well as constructive posteriors… (They seemed to mean constructible matching priors as far as I understood.)

The final talk in this session by Chuanhei Liu on a new approach (modestly!) called inferential model was incomprehensible, with the speaker repeatedly stating that the principles were too hard to explain in five minutes and needed an incoming book… I later took a brief look at an associated paper, which relates to fiducial inference and to Dempster’s belief functions. For me, it has the same Münchhausen feeling of creating a probability out of nothing, creating a distribution on the parameter by ignoring the fact that the fiducial equation x=a(θ,u) modifies the distribution of u once x is observed.

NIPS 2014

Posted in Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on December 15, 2014 by xi'an

mugSecond and last day of the NIPS workshops! The collection of topics was quite broad and would have made my choosing an ordeal, except that I was invited to give a talk at the probabilistic programming workshop, solving my dilemma… The first talk by Kathleen Fisher was quite enjoyable in that it gave a conceptual discussion of the motivations for probabilistic languages, drawing an analogy with the early days of computer programming that saw a separation between higher level computer languages and machine programming, with a compiler interface. And calling for a similar separation between the models faced by statistical inference and machine-learning and the corresponding code, if I understood her correctly. This was connected with Frank Wood’s talk of the previous day where he illustrated the concept through a generation of computer codes to approximately generate from standard distributions like Normal or Poisson. Approximately as in ABC, which is why the organisers invited me to talk in this session. However, I was a wee bit lost in the following talks and presumably lost part of my audience during my talk, as I realised later to my dismay when someone told me he had not perceived the distinction between the trees in the random forest procedure and the phylogenetic trees in the population genetic application. Still, while it had for me a sort of Twilight Zone feeling of having stepped in another dimension, attending this workshop was an worthwhile experiment as an eye-opener into a highly different albeit connected field, where code and simulator may take the place of a likelihood function… To the point of defining Hamiltonian Monte Carlo directly on the former, as Vikash Mansinghka showed me at the break.

I completed the day with the final talks in the variational inference workshop, if only to get back on firmer ground! Apart from attending my third talk by Vikash in the conference (but on a completely different topic on variational approximations for discrete particle-ar distributions), a talk by Tim Salimans linked MCMC and variational approximations, using MCMC and HMC to derive variational bounds. (He did not expand on the opposite use of variational approximations to build better proposals.) Overall, I found these two days and my first NIPS conference quite exciting, if somewhat overpowering, with a different atmosphere and a different pace compared with (small or large) statistical meetings. (And a staggering gender imbalance!)