Archive for the R Category

likelihood-free inference in high-dimensional models

Posted in Books, R, Statistics, University life with tags , , , , , , , , , on September 1, 2015 by xi'an

“…for a general linear model (GLM), a single linear function is a sufficient statistic for each associated parameter…”

Water Tower, Michigan Avenue, Chicago, Oct. 31, 2012The recently arXived paper “Likelihood-free inference in high-dimensional models“, by Kousathanas et al. (July 2015), proposes an ABC resolution of the dimensionality curse [when the dimension of the parameter and of the corresponding summary statistics] by turning Gibbs-like and by using a component-by-component ABC-MCMC update that allows for low dimensional statistics. In the (rare) event there exists a conditional sufficient statistic for each component of the parameter vector, the approach is just as justified as when using a generic ABC-Gibbs method based on the whole data. Otherwise, that is, when using a non-sufficient estimator of the corresponding component (as, e.g., in a generalised [not general!] linear model), the approach is less coherent as there is no joint target associated with the Gibbs moves. One may therefore wonder at the convergence properties of the resulting algorithm. The only safe case [in dimension 2] is when one of the restricted conditionals does not depend on the other parameter. Note also that each Gibbs step a priori requires the simulation of a new pseudo-dataset, which may be a major imposition on computing time. And that setting the tolerance for each parameter is a delicate calibration issue because in principle the tolerance should depend on the other component values. Continue reading

abcfr 0.9-3

Posted in R, Statistics, University life with tags , , , , , , , , on August 27, 2015 by xi'an

garden tree, Jan. 12, 2012In conjunction with our reliable ABC model choice via random forest paper, about to be resubmitted to Bioinformatics, we have contributed an R package called abcrf that produces a most likely model and its posterior probability out of an ABC reference table. In conjunction with the realisation that we could devise an approximation to the (ABC) posterior probability using a secondary random forest. “We” meaning Jean-Michel Marin and Pierre Pudlo, as I only acted as a beta tester!

abcrfThe package abcrf consists of three functions:

  • abcrf, which constructs a random forest from a reference table and returns an object of class `abc-rf’;
  • plot.abcrf, which gives both variable importance plot of a model choice abc-rf object and the projection of the reference table on the LDA axes;
  • predict.abcrf, which predict the model for new data and evaluate the posterior probability of the MAP.

An illustration from the manual:

data(snp)
data(snp.obs)
mc.rf <- abcrf(snp[1:1e3, 1], snp[1:1e3, -1])
predict(mc.rf, snp[1:1e3, -1], snp.obs)

Seattle histogram

Posted in pictures, R, Statistics, Travel with tags , , , on August 16, 2015 by xi'an

stritart3

STAN trailer [PG+53]

Posted in Kids, R, Statistics, University life with tags , , , , on August 14, 2015 by xi'an

[Heading off to mountainous areas with no Internet or phone connection, I posted a series of entries for the following week, starting with this brilliant trailer of Michael:]

JSM 2015 [day #2]

Posted in Books, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , on August 11, 2015 by xi'an

Today, at JSM 2015, in Seattle, I attended several Bayesian sessions, having sadly missed the Dennis Lindley memorial session yesterday, as it clashed with my own session. In the morning sessions on Bayesian model choice, David Rossell (Warwick) defended non-local priors à la Johnson (& Rossell) as having better frequentist properties. Although I appreciate the concept of eliminating a neighbourhood of the null in the alternative prior, even from a Bayesian viewpoint since it forces us to declare explicitly when the null is no longer acceptable, I find the asymptotic motivation for the prior less commendable and open to arbitrary choices that may lead to huge variations in the numerical value of the Bayes factor. Another talk by Jin Wang merged spike and slab with EM with bootstrap with random forests in variable selection. But I could not fathom what the intended properties of the method were… Besides returning another type of MAP.

The second Bayesian session of the morn was mostly centred on sparsity and penalisation, with Carlos Carvalho and Rob McCulloch discussing a two step method that goes through a standard posterior  construction on the saturated model, before using a utility function to select the pertinent variables. Separation of utility from prior was a novel concept for me, if not for Jay Kadane who objected to Rob a few years ago that he put in the prior what should be in the utility… New for me because I always considered the product prior x utility as the main brick in building the Bayesian edifice… Following Herman Rubin’s motto! Veronika Rocková linked with this post-LASSO perspective by studying spike & slab priors based on Laplace priors. While Veronicka’s goal was to achieve sparsity and consistency, this modelling made me wonder at the potential equivalent in our mixtures for testing approach. I concluded that having a mixture of two priors could be translated in a mixture over the sample with two different parameters, each with a different prior. A different topic, namely multiple testing, was treated by Jim Berger, who showed convincingly in my opinion that a Bayesian approach provides a significant advantage.

In the afternoon finalists of the ISBA Savage Award presented their PhD work, both in the theory and  methods section and in the application section. Besides Veronicka Rocková’s work on a Bayesian approach to factor analysis, with a remarkable resolution via a non-parametric Indian buffet prior and a variable selection interpretation that avoids MCMC difficulties, Vinayak Rao wrote his thesis on MCMC methods for jump processes with a finite number of observations, using a highly convincing completion scheme that created independence between blocks and which reminded me of the Papaspiliopoulos et al. (2005) trick for continuous time processes. I do wonder at the potential impact of this method for processing the coalescent trees in population genetics. Two talks dealt with inference on graphical models, Masanao Yajima and  Christine Peterson, inferring the structure of a sparse graph by Bayesian methods.  With applications in protein networks. And with again a spike & slab prior in Christine’s work. The last talk by Sayantan Banerjee was connected to most others in this Savage session in that it also dealt with sparsity. When estimating a large covariance matrix. (It is always interesting to try to spot tendencies in awards and conferences. Following the Bayesian non-parametric era, are we now entering the Bayesian sparsity era? We will see if this is the case at ISBA 2016!) And the winner is..?! We will know tomorrow night! In the meanwhile, congrats to my friends Sudipto Banerjee, Igor Prünster, Sylvia Richardson, and Judith Rousseau who got nominated IMS Fellows tonight.

JSM 2015 [day #1]

Posted in Books, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , on August 10, 2015 by xi'an

ferryThis afternoon, at JSM 2015, in Seattle, we had the Bayesian Computation I and II sessions that Omiros Papaspiliopoulos and myself put together (sponsored by IMS and ISBA). Despite this being Sunday and hence having some of the participants still arriving, the sessions went on well in terms of audience. Thanks to Mark Girolami’s strict presidency, we were so much on time in Bayesian Computation I that we had 20mn left for a floor discussion that turned into a speakers’ discussion! All talks were of obvious interest for MCMCists, but Ryan Adams’ presentation on firefly Monte Carlo got me thinking for most of the afternoon on different ways of exploiting the existence of a bound on the terms composing the target. With little to show by the end of the afternoon! On the mundane side, I was sorry to miss Pierre Jacob, who was still in France due to difficulties in obtaining a working visa for Harvard (!), and surprised to see Dawn Woodard wearing a Uber tee-shirt, until she told us she was now working at Uber! Which a posteriori makes sense, given her work on traffic predictions!

delayed in Seattle

Posted in Books, R, Statistics, Travel, University life with tags , , , , , , , , , , on August 9, 2015 by xi'an

Here are the slides of my talk on delayed acceptance I present this afternoon at JSM 2015, in Seattle, in the Bayesian Computation I (2pm, room CC-4C1) and II (4pm, room CC-3A) sessions Omiros Papaspiliopoulos and myself put together (sponsored by IMS and ISBA):

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