IMS workshop [day 3]

I made the “capital” mistake of walking across the entire NUS campus this morning, which is quite green and pretty, but which almost enjoys an additional dimension brought by such an intense humidity that one feels having to get around this humidity!, a feature I have managed to completely erase from my memory of my previous visit there. Anyway, nothing of any relevance. oNE talk in the morning was by Markus Eisenbach on tools used by physicists to speed up Monte Carlo methods, like the Wang-Landau flat histogram, towards computing the partition function, or the distribution of the energy levels, definitely addressing issues close to my interest, but somewhat beyond my reach for using a different language and stress, as often in physics. (I mean, as often in physics talks I attend.) An idea that came out clear to me was to bypass a (flat) histogram target and aim directly at a constant slope cdf for the energy levels. (But got scared away by the Fourier transforms!)

Lawrence Murray then discussed some features of the Birch probabilistic programming language he is currently developing, especially a fairly fascinating concept of delayed sampling, which connects with locally-optimal proposals and Rao Blackwellisation. Which I plan to get back to later [and hopefully sooner than later!].

In the afternoon, Maria de Iorio gave a talk about the construction of nonparametric priors that create dependence between a sequence of functions, a notion I had not thought of before, with an array of possibilities when using the stick breaking construction of Dirichlet processes.

And Christophe Andrieu gave a very smooth and helpful entry to partly deterministic Markov processes (PDMP) in preparation for talks he is giving next week for the continuation of the workshop at IMS. Starting with the guided random walk of Gustafson (1998), which extended a bit later into the non-reversible paper of Diaconis, Holmes, and Neal (2000). Although I had a vague idea of the contents of these papers, the role of the velocity ν became much clearer. And premonitory of the advances made by the more recent PDMP proposals. There is obviously a continuation with the equally pedagogical talk Christophe gave at MCqMC in Rennes two months [and half the globe] ago,  but the focus being somewhat different, it really felt like a new talk [my short term memory may also play some role in this feeling!, as I now remember the discussion of Hilderbrand (2002) for non-reversible processes]. An introduction to the topic I would recommend to anyone interested in this new branch of Monte Carlo simulation! To be followed by the most recently arXived hypocoercivity paper by Christophe and co-authors.

positions at QUT stats

Chris Drovandi sent me the information that the Statistics Group,  QUT, Brisbane, is advertising for three positions:

• Professor in Statistical Data Science (Remuneration package from $AUD206,729 per year)
• Lecturer in Statistical Data Science (Remuneration package of $AUD108,796 to $AUD129,209 per year)
• PhD Scholarship in Computational Bayesian Statistics ($AUD35,000 per year tax-free for 3 years, with an additional $AUD5,000 per year for project costs)

This is a great opportunity, a very active group, and a great location, which I visited several times, so if interested apply before October 1.

Bayesian model selection without evidence

“The new method circumvents the challenges associated with accurate evidence calculations by computing posterior odds ratios using Bayesian parameter estimation”

One paper leading to another, I had a look at Hee et al. 2015 paper on Bayes factor estimation. The “novelty” stands in introducing the model index as an extra parameter in a single model encompassing all models under comparison, the “new” parameterisation being in (θ,n) rather than in θ. With the distinction that the parameter θ is now made of the union of all parameters across all models. Which reminds us very much of Carlin and Chib (1995) approach to the problem. (Peter Green in his Biometrika (1995) paper on reversible jump MCMC uses instead a direct sum of parameter spaces.) The authors indeed suggest simulating jointly (θ,n) in an MCMC or nested sampling scheme. Rather than being updated by arbitrary transforms as in Carlin and Chib (1995) the useless parameters from the other models are kept constant… The goal being to estimate P(n|D) the marginal posterior on the model index, aka the posterior probability of model n.

Now, I am quite not certain keeping the other parameter constants is a valid move: given a uniform prior on n and an equally uniform proposal, the acceptance probability simplifies into the regular Metropolis-Hastings ratio for model n. Hence the move is valid within model n. If not, I presume the previous pair (θ⁰,n⁰) is repeated. Wait!, actually, this is slightly more elaborate: if a new value of n, m, is proposed, then the acceptance ratio involves the posteriors for both n⁰ and m, possibly only the likelihoods when the proposal is the prior. So the move will directly depend on the likelihood ratio in this simplified case, which indicates the scheme could be correct after all. Except that this neglects the measure theoretic subtleties that led to reversible jump symmetry and hence makes me wonder. In other words, it follows exactly the same pattern as reversible jump without the constraints of the latter… Free lunch,  anyone?!

Statistics & Computing [toc]

The latest [June] issue of Statistics & Computing is full of interesting Bayesian and Monte Carlo entries, some of which are even open access!

• Proximal Markov chain Monte Carlo algorithms
  Marcelo Pereyra Pages 745-760

  Download PDF (2992KB) View Article

• A computational procedure for estimation of the mixing time of the random-scan Metropolis algorithm
  David A. Spade Pages 761-781

  Download PDF (969KB) View Article

• Exact estimation of multiple directed acyclic graphs
  Chris J. Oates, Jim Q. Smith, Sach Mukherjee, James Cussens Pages 797-811

  Download PDF (932KB) View Article

• Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems
  Anindya Bhadra, Raymond J. Carroll Pages 827-840

  Download PDF (2605KB) View Article

• Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach
  Nadja Klein, Thomas Kneib Pages 841-860

  Download PDF (4572KB) View Article

• Computation of Gaussian orthant probabilities in high dimension
  James Ridgway Pages 899-916

  Download PDF (998KB) View Article

 

afternoon on Bayesian computation

Richard Everitt organises an afternoon workshop on Bayesian computation in Reading, UK, on April 19, the day before the Estimating Constant workshop in Warwick, following a successful afternoon last year. Here is the programme:

1230-1315  Antonietta Mira, Università della Svizzera italiana
1315-1345  Ingmar Schuster, Université Paris-Dauphine
1345-1415  Francois-Xavier Briol, University of Warwick
1415-1445  Jack Baker, University of Lancaster
1445-1515  Alexander Mihailov, University of Reading
1515-1545  Coffee break
1545-1630  Arnaud Doucet, University of Oxford
1630-1700  Philip Maybank, University of Reading
1700-1730  Elske van der Vaart, University of Reading
1730-1800  Reham Badawy, Aston University
1815-late  Pub and food (SCR, UoR campus)

and the general abstract:

The Bayesian approach to statistical inference has seen major successes in the past twenty years, finding application in many areas of science, engineering, finance and elsewhere. The main drivers of these successes were developments in Monte Carlo methods and the wide availability of desktop computers. More recently, the use of standard Monte Carlo methods has become infeasible due the size and complexity of data now available. This has been countered by the development of next-generation Monte Carlo techniques, which are the topic of this meeting.

The meeting takes place in the Nike Lecture Theatre, Agriculture Building [building number 59].

MCMskv, Lenzerheide, 4-7 Jan., 2016 [breaking news #6]

As indicated in an earlier MCMskv news, the scientific committee kept a session open for Breaking news! proposals, in conjunction with poster submissions. We received 21 proposals and managed to squeeze 12 fifteen minute presentations in an already tight program. (I advise all participants to take a relaxing New Year break and to load in vitamins and such in preparation for a 24/7 or rather 24/3 relentless and X’citing conference!) Here are the selected presentations, with (some links to my posts on the related papers and) abstracts available on the conference website. Note to all participants that there are still a few days left for submitting posters!

Luke Bornn

Jon Cockayne

Gersende Fort

Michael Gutmann

James Johndrow

Jean-Michel Marin

Murray Pollock

Maxim Rabinovich

Rebecca Steorts

Alexander Terenin

Yazhen Wang

Giacomo Zanella

MCMskv, Lenzerheide, 4-7 Jan., 2016 [news #5]

While the deadline for Breaking News! submission is now over, with close to 20 submissions!, there is a new opening for cheaper lodging: The CUBE hotel in Savognin (20km away) has an offer at 110 CHF per person and per night, including breakfast, dinner, and skipass in a room for 3 people (or more). Be sure to mention MCMski in the subject of your email. As mentioned in the previous post, there are other opportunities in nearby villages, for instance Tiefencastel, 11km away with a 19mn bus connection, or Chur, 18km away with a slower 39mn bus connection, but with a very wide range of offers.