Archive for July, 2011

JSM 2011

Posted in Running, Statistics, Travel, University life on July 31, 2011 by xi'an

Following Julien’s example, I am heading to Miami for JSM 2011 and take advantage of the looong if direct flight there to write a first post on attending JSM this year. The difficulty in such a large meeting is indeed in making a choice among the numerous parallel sessions to build a most profitable programme. Without turning it into an impossibility theorem. So [my] Rule #1 is to stick to a session for the whole time slot rather than trying to attend three talks in three different rooms. Rule #2 is to make one own’s programme from the on-line JSM site well in advance, ideally before starting your day. This way there is time to read the abstracts and to make a coherent choice. Rule #3: I would actually be less open-minded than Julien and opt for sessions whose title make sense to me, as 20 minutes is awfully short to grasp a new domain! Plenary sessions and special invited talks are obviously different in that the speaker has a much longer time to present an overview of one’s field and endeavours… Also take the time to read through the list of posters for keywords in your domains of interest: a random walk through the poster hall may have interesting outcomes, but it is more likely that you will miss the poster that was clearly related to your research.

Among the things I have spotted in my programme for this week in Miami, plenary talks by David Cox and Michael Jordan (Monday), Sylvia Richardson (Tuesday), and Michael Newton and Chris Holmes (Wednesday), the Savage Award session on Monday (I am sure Julien will attend! The model assessment session I organised is unfortunately scheduled at exactly the same time…), the SBSS mixer on Wednesday where prizes will be delivered. Enjoy your programme as well!!! (Sorry for the poor presentation, my Internet connection is just as poor!, and… btw avoid Enso on Lincoln Road Mall, drinks are outrageously overpriced! And, julien, running on the beach is fine if you plan it about 6am… This is the only free slot for the day anyway!)

When has Bayesian analysis really made a difference???

Posted in Books, Statistics, Travel, University life with tags , , , , , on July 30, 2011 by xi'an

With Kerrie Mengersen (QUT, Brisbane), we are launching a call for Bayesian “stories”, towards a collective paper/a special issue:

When has Bayesian analysis really made a difference?

Following the publication of “the theory that would not die” by Sharon McGrayne, about how Bayesian analysis contributed to science and the World in general, we [Kerrie Mengersen (QUT, Brisbane) and Christian Robert (Paris-Dauphine)] would like to put together a collection of six-page vignettes that describe real cases in which Bayesian analysis has been the only way to crack a really important problem.
To this end, we are launching a call for one page proposals that address the following questions.

  • What was the big problem to be solved? We mean big.
  • Why was it so difficult to solve statistically?
  • What was the Bayesian resolution?
  • Why couldn’t it be solved by other means? What were the shortcomings of other statistical solutions?
  • What was the overall impact of this Bayesian analysis on the real world?

We will then review those proposals and select the most significant ones towards the production of six page vignettes, aiming them to be published in a special issue or a multiple authored paper of a mainstream statistical journal. The deadline for the submission of a one-page proposal is September 30. It should be sent to Christian P. Robert at bayesianstatistics@gmailcom in pdf format. The final deadline will depend on the journal editor.

Obviously, if you happen to be like me at JSM 2011 this week and have a proposal (or journal!) in mind, feel free to talk to me about this! (I have also been waiting ages for a copy—two, actually—of the theory that would not die towards the dual goals of reading it and writing a review, but both channels failed to deliver.)

More book reviews!

Posted in Books, Statistics, University life with tags , , , on July 30, 2011 by xi'an

Last week Sam Behseta asked me to join the editorial board of CHANCE as the book editor and I frankly see no reason to refuse the offer! First, it means more books to read and review (hence, free material for the ‘Og!). Second, CHANCE is a general audience statistical journal published by the ASA, hence completely reputable!, and parallel to Significance. Third, it is a fairly pleasant way (for me at least, if not uniformly for the authors) to contribute to the society.

Le Monde puzzle [#29]

Posted in R, Statistics with tags , , on July 29, 2011 by xi'an

This week, the puzzle from the weekend edition of Le Monde was easy to state: in the sequence (8+17n), is there a 6th power? a 7th? an 8th? If so, give the first occurrence. So I first wrote an R code for a function testing whether an integer is any power:

ispower=function(x){
ispo=FALSE
logx=log(x)
i=trunc(logx/log(2))
while((i>1)&&(!ispo)){
j=t=trunc(exp(logx/i))
while (t<x) t=j*t
ispo=(x==t)
if (!ispo){
j=t=j+1
while (t<x) t=j*t
ispo=(x==t)}
i=i-1}
list(is=ispo,pow=j)}

(The function returns the highest possible power.) Then I ran the thing over the first million of values of the sequence:

fib=8
for (j in 1:10^6){
fib=fib+17
tes=ispower(fib)
if (tes$is)
print(c(fib,tes$pow,log(fib)/log(tes$pow)))}

only to find that only the powers 2,3,6,10,11,19 were present among the first terms. Continue reading

Core not in CiRM

Posted in Books, R, Statistics, University life with tags , , , , , , on July 28, 2011 by xi'an

Despite not enjoying this year the optimal environment of CiRM, we are still making good progress on the revision (or the R vision) of Bayesian Core. In the past two days, we went over Chapters 1 (Introduction), 2 (Normal Models), 5 (Capture-Recapture Experiments), and 6 (Mixture Models), with Chapters 3 (Regression), 4 (Generalised Linear Models) and 9 (Image Analysis) being close to completion. While having a “last”go at the R tutorial part of Chapter 1, I came across this paragraph

One of the most frustrating features of R is that the graphical device is not refreshed while a program is executed in the main window. This implies that, if you switch from one terminal to another or if the screen saver starts, the whole or parts of the graph currently on the graphical device will not be visible until the completion of the program. Conversely, refreshing very large graphs will delay the activation of the prompt >.

that I very gladly deleted, as the current 2.11.1 version of R does no longer suffer from this painful freeze in the graphics (at least on my Kubuntu 10.10 version).

Actually, I do not think I mentioned it in a previous post: our new edition will be called Bayesian Essentials with R. Both to distinguish it from Bayesian Core (as it should be published in the Use R! series) and because it appeared (thanks to colleagues and readers) that core did not sound very appealing to English-speaking audiences looking for a statistics book…

A slice of infinity

Posted in R, Statistics, University life with tags , , , , , , , on July 28, 2011 by xi'an

Peng Yu sent me an email about the conditions for convergence of a Gibbs sampler:

The following statement mentions convergence. But I’m not familiar what the regularity condition is.

“But it is necessary to have a finite probability of moving away from the current state at all times in order to satisfy the regularity conditions on which the whole MCMC theory depends.”

Slice sampler is discussed in your book Monte Carlo Statistical Methods. I think that the “regularity condition” may have been discussed in your book. If so, would you please let me know where it is? Thanks and look forward to hearing from you!

The quote is from Martyn Plummer and deals with a stopping rule in JAGS implementation of the slice sampler. (The correct wording should be “strictly positive probability” rather than “finite probability”, I think.) However, this has nothing to do with a “regularity condition” on the irreducibility of a Markov chain: if a slice sampler is implemented for an unbounded density target, say a Beta(1/2,1/2), there is no irreducibility condition connected with the infiniteness of the density. In theory, (a) the chain never visits the “state” where the density is infinite (if only because we are dealing with a continuous state space) and (b) after visiting a value x with a large density f(x), the slice sampler allows for a move away from it since the slice involves a uniform simulation over (0,f(x)). Deeper properties of the slice sampler (like geometric ergodicity) are explored in, e.g., this JRSS B paper by Gareth Roberts and Jeff Rosenthal and this one in the Annals of Statistics by Radford Neal. In practice, the problem is caused by values of f(x) that cannot be computed and hence produce an error message like

Singularity in likelihood found by Slicer.

If those singularities can be localised, a neighbourhood excluding them should be introduced. (More easily said than done, obviously!)

Here is an example of a slice sampler with the Beta(1/2,1/2) distribution:

#graphics
dote=function(x,y) points(x,y,col="gold",pch=19,cex=.4)
mote=function(x,y,z,w) lines(c(x,z),c(y,w),col="gold",lwd=.5)
cst=dbeta(.5,.5,.5)*.5 #normalising constant
#inverting f(x)=d, 2nd degree equation
hitden=function(d) .5+.5*sqrt(1-4*( cst/ max(d,dbeta(.5,.5,.5)))^2)*c(-1,1)
#output
curve(dbeta(x,.5,.5),0,1,ylab="density",lwd=2,col="steelblue",n=1001)
x=runif(1);u=runif(1)*dbeta(x,.5,.5);dote(x,u)
for (t in 1:100){ #100 slice steps
   bo=hitden(u)
   nx=sample(c(runif(1,0,bo[1]),runif(1,bo[2],1)),1)
   nu=runif(1)*dbeta(nx,.5,.5)
   mote(x,u,nx,nu)
   x=nx;u=nu;dote(x,u)
   }

which clearly explores the whole area under the Beta(1/2,1/2) density. Even when started at a large density value like f(.999999), it eventually leaves the vicinity of this highly improbable value.

Xiao-Li Meng’s inception [in Paris]

Posted in Statistics, University life with tags , , , , , on July 27, 2011 by xi'an

Xiao-Li Meng will give a talk in Paris next September 1st, so I advertise it now, before my Parisian readers leave the city for their August retreat. Here is the abstract, explaining the above title:

Statistical Inception for the MCMC Dream: The kick is in the residual (augmentation)!

Xiao-Li Meng

Department of Statistics, Harvard University

The development of MCMC algorithms via data augmentation (DA) or equivalently auxiliary variables has some resemblance to the theme plot of the recent Hollywood hit Inception. We MCMC designers all share essentially the same “3S” dream, that is, to create algorithms that are simple, stable, and speedy. Within that grand dream, however, we have created a rather complex web of tools, with some of them producing very similar algorithms but for unclear reasons, or others that were thought to be of different origins but actually are layered when viewed from a suitable distance. These include conditional augmentation, marginal augmentation, PX-DA, partially non-centering parameterization, sandwiched algorithms, interweaving strategies, ASIS, etc. It turns out that there is a simple statistical insight that can unify essentially all these methods conceptually, and it also provides practical guidelines for their DA constructions. It is the simple concept of regression residuals, which are constructed to be orthogonal to the regression functions. All these methods in one form or another effectively build a residual augmentation. Given a DA distribution f(T, A), where T is our targeted variable (i.e., f(T) is our targeted distribution) and A is the augmented variable, there are two broad classes of residuals depending on whether we regress T on A or A on T. In this talk we will demonstrate how methods like conditional augmentation and partially non-centering parameterization build their residual augmentations by regressing A on T, whereas methods such as marginal augmentation and ASIS effectively use residual augmentations from regressing T on A. For either class, the attempted orthogonality helps to reduce the dependence among MCMC draws, and when the orthogonality leads to true independence as occurring in some special cases, we reach the dream of producing i.i.d. draws. (The talk is based on an upcoming discussion article, especially its rejoinder, Yu and Meng (2011, JCGS) )

The talk will take place at Institut Henri Poincaré, Thursday Sept. 1, at 15:00, as part of the Big’MC seminars.

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