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.

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

As the deadline draws near, a week from now!, I want to remind participants to the next MCMSki conference in Lenzerheide that they can candidate to the Breaking News! session:

This edition of the MCMSki conference will include a Breaking News! session, covering the latest developments in the field, latest enough to be missed by the scientific committee when building the program. To be considered for this special session, please indicate you wish to compete for this distinction when submitting your poster. The deadline for submission is November 15, 2015. The selection will be made by the scientific committee and the time allocated to each talk will depend on the number of selected talks. Selected presenters will be notified by December 02, 2015, and they are expected to participate in the poster session to ensure maximal dissemination of their breaking news.

And since I got personal enquiries yesterday, the number of talks during that session will be limited to have real talks and not flash oral presentations of incoming posters. Unless the scientific committee cannot make its mind on which news to break..!

MCMskv, Lenzerheide, 4-7 Jan., 2016 on a shoestring [news #3]

As the ‘Og received several comments about the accommodation costs for BayesComp MCMski V, which are indeed rather high if one only follows the suggestions on the lodging webpage, I started checking for cheaper alternatives in Lenzerheide and around. On booking.com, I found several local hotels and studios from 100€ to 200€ per night for two or three guests, with breakfast included. The offer on airbnb was quite limited but I still managed to secure a small chalet at about 50€ per person and per night. There are more opportunities in nearby villages, for instance Tiefencastel, 11km away with a 19mn bus connection. Chur is 18km away with a slower 39mn bus connection, but with a very wide range of offers. Savognin, near the pricey Sankt Moritz is 20km away, with other cheap alternatives. Which may even make renting a car worth the expense if split between 3 or 4. Note also that low-cost airlines fly to Zürich from major European cities. For instance, Easyjet is currently offering a round trip from London for 72€…