Archive for ABC

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)

consistency of ABC

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on August 25, 2015 by xi'an

Along with David Frazier and Gael Martin from Monash University, Melbourne, we have just completed (and arXived) a paper on the (Bayesian) consistency of ABC methods, producing sufficient conditions on the summary statistics to ensure consistency of the ABC posterior. Consistency in the sense of the prior concentrating at the true value of the parameter when the sample size and the inverse tolerance (intolerance?!) go to infinity. The conditions are essentially that the summary statistics concentrates around its mean and that this mean identifies the parameter. They are thus weaker conditions than those found earlier consistency results where the authors considered convergence to the genuine posterior distribution (given the summary), as for instance in Biau et al. (2014) or Li and Fearnhead (2015). We do not require here a specific rate of decrease to zero for the tolerance ε. But still they do not hold all the time, as shown for the MA(2) example and its first two autocorrelation summaries, example we started using in the Marin et al. (2011) survey. We further propose a consistency assessment based on the main consistency theorem, namely that the ABC-based estimates of the marginal posterior densities for the parameters should vary little when adding extra components to the summary statistic, densities estimated from simulated data. And that the mean of the resulting summary statistic is indeed one-to-one. This may sound somewhat similar to the stepwise search algorithm of Joyce and Marjoram (2008), but those authors aim at obtaining a vector of summary statistics that is as informative as possible. We also examine the consistency conditions when using an auxiliary model as in indirect inference. For instance, when using an AR(2) auxiliary model for estimating an MA(2) model. And ODEs.

ABC à… Montréal

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on August 24, 2015 by xi'an

Montreal1Like last year, NIPS will be hosted in Montréal, Québec, Canada, and like last year there will be an ACB NIPS workshop. With a wide variety of speakers and poster presenters. There will also be a probabilistic integration NIPS workshop, to which I have been invited to give a talk, following my blog on the topic! Workshops are on December 11 and 12, and I hope those two won’t overlap so that I can enjoy both at length (before flying back to London for CFE 2015…)

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.

astronomical evidence

Posted in pictures, Statistics, University life with tags , , , , , , , , , , , , on July 24, 2015 by xi'an

As I have a huge arXiv backlog and an even higher non-arXiv backlog, I cannot be certain I will find time to comment on those three recent and quite exciting postings connecting ABC with astro- and cosmo-statistics [thanks to Ewan for pointing out those to me!]:

Measuring statistical evidence using relative belief [book review]

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , , , , on July 22, 2015 by xi'an

“It is necessary to be vigilant to ensure that attempts to be mathematically general do not lead us to introduce absurdities into discussions of inference.” (p.8)

This new book by Michael Evans (Toronto) summarises his views on statistical evidence (expanded in a large number of papers), which are a quite unique mix of Bayesian  principles and less-Bayesian methodologies. I am quite glad I could receive a version of the book before it was published by CRC Press, thanks to Rob Carver (and Keith O’Rourke for warning me about it). [Warning: this is a rather long review and post, so readers may chose to opt out now!]

“The Bayes factor does not behave appropriately as a measure of belief, but it does behave appropriately as a measure of evidence.” (p.87)

Continue reading

MCMskv, Lenzerheide, 4-7 Jan., 2016 [news #1]

Posted in Kids, Mountains, pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , on July 20, 2015 by xi'an

moonriseThe BayesComp MCMski V [or MCMskv for short] has now its official website, once again maintained by Merrill Lietchy from Drexel University, Philadelphia, and registration is even open! The call for contributed sessions is now over, while the call for posters remains open until the very end. The novelty from the previous post is that there will be a “Breaking news” [in-between the Late news sessions at JSM and the crash poster talks at machine-learning conferences] session to highlight major advances among poster submissions. And that there will be an opening talk by Steve [the Bayesian] Scott on the 4th, about the frightening prospect of MCMC death!, followed by a round-table and a welcome reception, sponsored by the Swiss Supercomputing Centre. Hence the change in dates. Which still allows for arrivals in Zürich on the January 4th [be with you].

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