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high-dimensional stochastic simulation and optimisation in image processing [day #2]

Posted in pictures, Statistics, Travel, Uncategorized, University life, Wines with tags , , , , , , on August 30, 2014 by xi'an

After a nice morning run down Leigh Woods and on the muddy banks of the Avon river, I attended a morning session on hyperspectral image non-linear modelling. Topic about which I knew nothing beforehand. Hyperspectral images are 3-D images made of several wavelengths to improve their classification as a mixture of several elements. The non-linearity is due to the multiple reflections from the ground as well as imperfections in the data collection. I found this new setting of clear interest, from using mixtures to exploring Gaussian processes and Hamiltonian Monte Carlo techniques on constrained spaces… Not to mention the “debate” about using Bayesian inference versus optimisation. It was overall a day of discovery as I am unaware of the image processing community (being the outlier in this workshop!) and of their techniques. The problems mostly qualify as partly linear high-dimension inverse problems, with rather standard if sometimes hybrid MCMC solutions. (The day ended even more nicely with another long run in the fields of Ashton Court and a conference diner by the river…)

 

high-dimensional stochastic simulation and optimisation in image processing [day #1]

Posted in pictures, Statistics, Travel, Uncategorized, University life, Wines with tags , , , , , , , , , , , on August 29, 2014 by xi'an

Even though I flew through Birmingham (and had to endure the fundamental randomness of trains in Britain), I managed to reach the “High-dimensional Stochastic Simulation and Optimisation in Image Processing” conference location (in Goldney Hall Orangery) in due time to attend the (second) talk by Christophe Andrieu. He started with an explanation of the notion of controlled Markov chain, which reminded me of our early and famous-if-unpublished paper on controlled MCMC. (The label “controlled” was inspired by Peter Green who pointed out to us the different meanings of controlled in French [meaning checked or monitored] and in English . We use it here in the English sense, obviously.) The main focus of the talk was on the stability of controlled Markov chains. With of course connections with out controlled MCMC of old, for instance the case of the coerced acceptance probability. Which happened to be not that stable! With the central tool being Lyapounov functions. (Making me wonder whether or not it would make sense to envision the meta-problem of adaptively estimating the adequate Lyapounov function from the MCMC outcome.)

As I had difficulties following the details of the convex optimisation talks in the afternoon, I eloped to work on my own and returned to the posters & wine session, where the small number of posters allowed for the proper amount of interaction with the speakers! Talking about the relevance of variational Bayes approximations and of possible tools to assess it, about the use of new metrics for MALA and of possible extensions to Hamiltonian Monte Carlo, about Bayesian modellings of fMRI and of possible applications of ABC in this framework. (No memorable wine to make the ‘Og!) Then a quick if reasonably hot curry and it was already bed-time after a rather long and well-filled day!z

L’Affiche Rouge (Feb. 21, 1944)

Posted in Uncategorized with tags , , , , , on February 21, 2014 by xi'an

my week at War[wick]

Posted in pictures, Running, Statistics, Travel, Uncategorized with tags , , , , , , , , , on February 1, 2014 by xi'an

This was a most busy and profitable week in Warwick as, in addition to meeting with local researchers and students on a wide range of questions and projects, giving an extended seminar to MASDOC students, attending as many seminars as humanly possible (!), and preparing a 5k race by running in the Warwickshire countryside (in the dark and in the rain), I received the visits of Kerrie Mengersen, Judith Rousseau and Jean-Michel Marin, with whom I made some progress on papers we are writing together. In particular, Jean-Michel and I wrote the skeleton of a paper we (still) plan to submit to COLT 2014 next week. And Judith, Kerrie and I drafted new if paradoxical aconnections between empirical likelihood and model selection. Jean-Michel and Judith also gave talks at the CRiSM seminar, Jean-Michel presenting the latest developments on the convergence of our AMIS algorithm, Judith summarising several papers on the analysis of empirical Bayes methods in non-parametric settings.

2013 in review [by WordPress]

Posted in Uncategorized with tags , on December 31, 2013 by xi'an

The WordPress.com stats helper monkeys prepared a 2013 annual report for this blog.

Here’s an excerpt:

The Louvre Museum has 8.5 million visitors per year. This blog was viewed about 250,000 times in 2013. If it were an exhibit at the Louvre Museum, it would take about 11 days for that many people to see it.

Click here to see the complete report.

beta HPD

Posted in Books, R, Statistics, Uncategorized, University life with tags , , , , , , , on October 17, 2013 by xi'an

While writing an introductory chapter on Bayesian analysis (in French), I came by the issue of computing an HPD region when the posterior distribution is a Beta B(α,β) distribution… There is no analytic solution and hence I resorted to numerical resolution (provided here for α=117.5, β=115.5):

f=function(p){

  # find the symmetric
  g=function(x){return(x-p*((1-p)/(1-x))^(115.5/117.5))}
  return(uniroot(g,c(.504,.99))$root)}

ff=function(alpha){

  # find the coverage
  g=function(x){return(x-p*((1-p)/(1-x))^(115.5/117.5))}
  return(uniroot(g,c(.011,.49))$root)}

and got the following return:

> ff(.95)
[1] 0.4504879
> f(ff(.95))
[1] 0.5580267

which was enough for my simple book illustration… Since (.450,558) is then the HPD region at credible level 0.95.

Deborah Mayo’s talk in Montréal (JSM 2013)

Posted in Books, Statistics, Uncategorized with tags , , , , , , on July 31, 2013 by xi'an

As posted on her blog, Deborah Mayo is giving a lecture at JSM 2013 in Montréal about why Birnbaum’s derivation of the Strong Likelihood Principle (SLP) is wrong. Or, more accurately, why “WCP entails SLP”. It would have been a great opportunity to hear Deborah presenting her case and I am sorry I am missing this opportunity. (Although not sorry to be in the beautiful Dolomites at that time.) Here are the slides:

Deborah’s argument is the same as previously: there is no reason for the inference in the mixed (or Birnbaumized) experiment to be equal to the inference in the conditional experiment. As previously, I do not get it: the weak conditionality principle (WCP) implies that inference from the mixture output, once we know which component is used (hence rejecting the “and we don’t know which” on slide 8), should only be dependent on that component. I also fail to understand why either WCP or the Birnbaum experiment refers to a mixture (sl.13) in that the index of the experiment is assumed to be known, contrary to mixtures. Thus (still referring at slide 13), the presentation of Birnbaum’s experiment is erroneous. It is indeed impossible to force the outcome of y* if tail and of x* if head but it is possible to choose the experiment index at random, 1 versus 2, and then, if y* is observed, to report (E1,x*) as a sufficient statistic. (Incidentally, there is a typo on slide 15, it should be “likewise for x*”.)

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