Archive for population genetics

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!)

a bootstrap likelihood approach to Bayesian computation

Posted in Books, R, Statistics, University life with tags , , , , , , , , on October 16, 2014 by xi'an

This paper by Weixuan Zhu, Juan Miguel Marín [from Carlos III in Madrid, not to be confused with Jean-Michel Marin, from Montpellier!], and Fabrizio Leisen proposes an alternative to our 2013 PNAS paper with Kerrie Mengersen and Pierre Pudlo on empirical likelihood ABC, or BCel. The alternative is based on Davison, Hinkley and Worton’s (1992) bootstrap likelihood, which relies on a double-bootstrap to produce a non-parametric estimate of the distribution of a given estimator of the parameter θ. Including a smooth curve-fitting algorithm step, for which not much description is available from the paper.

“…in contrast with the empirical likelihood method, the bootstrap likelihood doesn’t require any set of subjective constrains taking advantage from the bootstrap methodology. This makes the algorithm an automatic and reliable procedure where only a few parameters need to be specified.”

The spirit is indeed quite similar to ours in that a non-parametric substitute plays the role of the actual likelihood, with no correction for the substitution. Both approaches are convergent, with similar or identical convergence speeds. While the empirical likelihood relies on a choice of parameter identifying constraints, the bootstrap version starts directly from the [subjectively] chosen estimator of θ. For it indeed needs to be chosen. And computed.

“Another benefit of using the bootstrap likelihood (…) is that the construction of bootstrap likelihood could be done once and not at every iteration as the empirical likelihood. This leads to significant improvement in the computing time when different priors are compared.”

This is an improvement that could apply to the empirical likelihood approach, as well, once a large enough collection of likelihood values has been gathered. But only in small enough dimensions where smooth curve-fitting algorithms can operate. The same criticism applying to the derivation of a non-parametric density estimate for the distribution of the estimator of θ. Critically, the paper only processes examples with a few parameters.

In the comparisons between BCel and BCbl that are produced in the paper, the gain is indeed towards BCbl. Since this paper is mostly based on examples and illustrations, not unlike ours, I would like to see more details on the calibration of the non-parametric methods and of regular ABC, as well as on the computing time. And the variability of both methods on more than a single Monte Carlo experiment.

I am however uncertain as to how the authors process the population genetic example. They refer to the composite likelihood used in our paper to set the moment equations. Since this is not the true likelihood, how do the authors select their parameter estimates in the double-bootstrap experiment? The inclusion of Crakel’s and Flegal’s (2013) bivariate Beta, is somewhat superfluous as this example sounds to me like an artificial setting.

In the case of the Ising model, maybe the pre-processing step in our paper with Matt Moores could be compared with the other algorithms. In terms of BCbl, how does the bootstrap operate on an Ising model, i.e. (a) how does one subsample pixels and (b)what are the validity guarantees?

A test that would be of interest is to start from a standard ABC solution and use this solution as the reference estimator of θ, then proceeding to apply BCbl for that estimator. Given that the reference table would have to be produced only once, this would not necessarily increase the computational cost by a large amount…

Bayesian introductions at IXXI

Posted in Mountains, Statistics, Travel, University life with tags , , , , , , on October 28, 2013 by xi'an

Ten days ago I did a lighting-fast visit to Grenoble for a quick introduction to Bayesian notions during a Bayesian day organised by Michael Blum. It was supported by IXXI, Rhône Alpes Complex Systems Institute, a light structure that favors interdisciplinary research to model complex sytems such as biological or social systems, technological networks… This was an opportunity to recycle my Budapest overview from Bayes 250th to Bayes 2.5.0. (As I have changed my email signature initial from X to IX, I further enjoyed the name IXXI!) More seriously, I appreciated (despite the too short time spent there!) the mix of perspectives and disciplines represented in this introduction, from Bayesian networks and causality in computer science and medical expert systems, to neurosciences and the Bayesian theory of mind, to Bayesian population genetics. And hence the mix of audiences. The part about neurosciences and social representations on others’ mind reminded me of the discussion with Pierre Bessières we had a year ago on France Culture. Again, I am quite sorry and apologetic for having missed part of the day and opportunities for discussions, simply because of a tight schedule this week…

Albert Jacquard (1925-2013)

Posted in Books, Statistics with tags , , , , , , on September 21, 2013 by xi'an

Albert Jacquard passed away last week. He was a humanist, engaged in the defence of outcasts (laissés pour compte) like homeless and illegal immigrants. He had a regular chronicle of two minutes on France Culture that I used to listen to (when driving at that time of the day). In the obituaries published in the recent days, this side of the character was put forward, while very little was said about his scientific legacy. He was a statistician, first at INSEE, then at INED. After getting a PhD in genetics from Stanford in 1968, he got back to INED as a population geneticist, writing in 1978 his most famous book, Éloge de la Différence, against racial theories, which is the first in a long series of vulgarisation and philosophical books. Among his scientific books, he wrote the entry on Probabilités in the popular vulgarisation series “Que Sais-Je?”, with more than 40,000 copies sold and used by generations of students. (Among its 125 pages, the imposed length for a  “Que Sais-Je?”, the book includes Bayes theorem and, more importantly, the Bayesian approach to estimating unknown probabilities!)

inference in Kingman’s coalescent with pMCMC

Posted in Books, Statistics, University life with tags , , , , , , , on May 22, 2013 by xi'an

As I was checking the recent stat postings on arXiv, I noticed the paper by Chen and Xie entitled inference in Kingman’s coalescent with pMCMC.  (And surprisingly deposited in the machine learning subdomain.) The authors compare a pMCMC implementation for Kingman’s coalescent with importance sampling (à la Stephens & Donnelly), regular MCMC and SMC.  The specifics of their pMCMC algorithm is that they simulate the coalescent times conditional on the tree structure and the tree structure conditional on the coalescent times (via SMC). The results reported in the paper consider up to five loci and agree with earlier experiments showing poor performances of MCMC algorithms (based on the LAMARC software and apparently using independent proposals).  They show similar performances between importance sampling and pMCMC. While I find this application of pMCMC interesting, I wonder at the generality of the approach: when I was introduced to ABC techniques, the motivation was that importance sampling was deteriorating very quickly with the number of parameters. Here it seems the authors only considered one parameter θ. I wonder what happens when the number of parameters increases. And how pMCMC would then compare with ABC.