This week I’ll start my Bayesian Statistics master’s course at the Collegio Carlo Alberto. I realized that some of last year students got PhD positions in prestigious US universities. So I thought that letting this year’s students have a first grasp of some great Bayesian papers wouldn’t do harm. The idea is that in addition to the course, the students will pick a paper from a list and present it (or rather part of it) to the others and to me. Which will let them earn some extra points for the final exam mark. It’s in the spirit of Xian’s Reading Classics Seminar (his list here).
I’ve made up the list below, inspired by two textbooks references lists and biased by personal tastes: Xian’s Bayesian Choice and Peter Hoff’s First Course in Bayesian Statistical Methods. See the pdf list and zipped folder for papers. Comments on the list are much welcome!
PS: reference n°1 isn’t a joke!
This is an article intended for the ISBA bulletin, jointly written by us all at Statisfaction, Rasmus Bååth from Publishable Stuff, Boris Hejblum from Research side effects, Thiago G. Martins from tgmstat@wordpress, Ewan Cameron from Another Astrostatistics Blog and Gregory Gandenberger from gandenberger.org.
Inspired by established blogs, such as the popular Statistical Modeling, Causal Inference, and Social Science or Xi’an’s Og, each of us began blogging as a way to diarize our learning adventures, to share bits of R code or LaTeX tips, and to advertise our own papers and projects. Along the way we’ve come to a new appreciation of the world of academic blogging: a never-ending international seminar, attended by renowned scientists and anonymous users alike. Here we share our experiences by weighing the pros and cons of blogging from the point of view of young researchers.
Mathieu and I have just realised that the version of our SQMC paper made available on the RSS web site contains several unfortunate typos. In particular, the symbol for “small o” has been replaced by a “big O” by editors. For instance, Theorem 9 should state the QMC beats standard SMC; i.e. the MSE (mean square error) of an SQMC estimator is
but in the RSS version, it reads
Well, that’s a bummer. For now, I recommend anyone to read instead the arxiv version (updated on Monday).
Almost 10 months since my latest post? I guess bloggin’ ain’t my thing… In my defense, Mathieu Gerber and I were quite busy revising our SQMC paper. I am happy to announce that it has just been accepted as a read paper in JRSSB. If all goes as planned, we should present the paper at the RSS ordinary meeting on Dec 10. Everybody is welcome to attend, and submit an oral or written discussion (or both). More details soon, when the event is officially announced on the RSS web-site.
What is SQMC? It is a QMC (Quasi-Monte Carlo) version of particle filtering. For the same CPU cost, it typically generates much more accurate estimators. Interested? consider reading the paper here (more recent version coming soon), checking this video where I present SQMC, or, even better, attending our talk in London!
I presented an arxived paper of my postdoc at the big success Young Bayesian Conference in Vienna. The big picture of the talk is simple: there are situations in Bayesian nonparametrics where you don’t know how to sample from the posterior distribution, but you can only compute posterior expectations (so-called marginal methods). So e.g. you cannot provide credible intervals. But sometimes all the moments of the posterior distribution are available as posterior expectations. So morally, you should be able to say more about the posterior distribution than just reporting the posterior mean. To be more specific, we consider a hazard (h) mixture model
where is a kernel, and the mixing distribution is random and discrete (Bayesian nonparametric approach).
We consider the survival function which is recovered from the hazard rate by the transform
and some possibly censored survival data having survival . Then it turns out that all the posterior moments of the survival curve evaluated at any time can be computed.
The nice trick of the paper is to use the representation of a distribution in a [Jacobi polynomial] basis where the coefficients are linear combinations of the moments. So one can sample from [an approximation of] the posterior, and with a posterior sample we can do everything! Including credible intervals.
I’ve wrapped up the few lines of code in an R package called momentify (not on CRAN). With a sequence of moments of a random variable supported on [0,1] as an input, the package does two things:
- evaluates the approximate density
- samples from it
A package example for a mixture of beta and 2 to 7 moments gives that result:
With Alexandre Thiéry we’ve been working on non-negative unbiased estimators for a while now. Since I’ve been talking about it at conferences and since we’ve just arXived the second version of the article, it’s time for a blog post. This post is kind of a follow-up of a previous post from July, where I was commenting on Playing Russian Roulette with Intractable Likelihoods by Mark Girolami, Anne-Marie Lyne, Heiko Strathmann, Daniel Simpson, Yves Atchade.
It’s been a while I haven’t written about parallelization and GPUs. With colleagues Lawrence Murray and Anthony Lee we have just arXived a new version of Parallel resampling in the particle filter. The setting is that, on modern computing architectures such as GPUs, thousands of operations can be performed in parallel (i.e. simultaneously) and therefore the rest of the calculations that cannot be parallelized quickly becomes the bottleneck. In the case of the particle filter (or any sequential Monte Carlo method such as SMC samplers), that bottleneck is the resampling step. The article investigates this issue and numerically compares different resampling schemes.
Today I am going to introduce the moustache target distribution (moustarget distribution for brievety). Load some packages first.
library(wesanderson) # on CRAN library(RShapeTarget) # available on https://github.com/pierrejacob/RShapeTarget/ library(PAWL) # on CRAN
Let’s invoke the moustarget distribution.
shape <- create_target_from_shape( file_name=system.file(package = "RShapeTarget", "extdata/moustache.svg"), lambda=5) rinit <- function(size) matrix(rnorm(2*size), ncol = 2) moustarget <- target(name = "moustache", dimension = 2, rinit = rinit, logdensity = shape$logd, parameters = shape$algo_parameters)
This defines a target distribution represented by a SVG file using RShapeTarget. The target probability density function is defined on and is proportional to on the segments described in the SVG files, and decreases exponentially fast to away from the segments. The density function of the moustarget is plotted below, a picture being worth a thousand words.
There’s a nice exhibition open until May 26th at the British Library in London, entitled Beautiful Science: Picturing Data, Inspiring Insight. Various examples of data visualizations are shown, either historical or very modern, or even made especially for the exhibition. Definitely worth a detour if you happen to be in the area, you can see everything in 15 minutes.
In particular there are nice visualisations of historical climate data, gathered from the logbooks of the English East India company, whose ships were crossing every possible sea in the beginning of the 19th century. The logbooks contain locations and daily weather reports, handwritten by the captains themselves. Turns out the logbooks are kept at the British Library itself and some of them are on display at the exhibition. More info on that project here: oldweather.org.
Kudos to Rasmus for this very practical approach, potentially very impactful. Maybe someday people will have to specify if they want a frequentist approach and not the other way around! (I had a dream, etc).