## Bayesian model comparison with vague or improper priors

Hi,

With Stephane Shao, Jie Ding and Vahid Tarokh we have just arXived a tech report entitled “Bayesian model comparison with the Hyvärinen score: computation and consistency“. Here I’ll explain the context, that is, scoring rules and Hyvärinen scores (originating in Hyvärinen’s score matching approach to inference), and then what we actually do in the paper.

## Dynamic publication list for research webpage using arXiv, HAL, or bibtex2html

Well of course, dynamic is conditional upon some manual feeding. If you put your papers on arXiv or HAL, then those two propose dynamic widgets. If you maintain a .bib file of your papers, you can use tools like bibtex2html. This is not dynamic at all, but it allows for finer tuning of url links you might want to add than with arXiv or HAL options. I review below those three options. (more…)

## ISBA elections, let’s go voting

The International Society for Bayesian Analysis (ISBA), is running elections until November, 15. This year, two contributors on this blog, Nicolas Chopin and myself, are running for an ISBA Section office. The sections of the society, nine in number as of today, gather researchers with common research interests: Computation, Objective Bayes, Nonparametrics, etc.

Here are our candidate statements:

## Approximating the cut distribution

Hi,

This post is about computational issues with the cut distribution for Bayesian inference in misspecified models. Some motivation was given in a previous post about a recent paper on modular Bayesian inference. The cut distribution, or variants of it, might play an important role in combining statistical models, especially in settings where one wants to propagate uncertainty while preventing misspecification from damaging estimation. The cut distribution can also be seen as a probabilistic analog of two-step point estimators. So the cut distribution is more than just a trick! And it raises interesting computational issues which I’ll describe here along with a solution via unbiased MCMC.

## Unbiased Hamiltonian Monte Carlo with couplings

With Jeremy Heng we have recently arXived a paper describing how to remove the burn-in bias of Hamiltonian Monte Carlo (HMC). This follows a recent work on unbiased MCMC estimators in general on which I blogged here. The case of HMC requires a specific yet very simple coupling. A direct consequence of this work is that Hamiltonian Monte Carlo can be massively parallelized: instead of running one chain for many iterations, one can run short coupled chains independently in parallel. The proposed estimators are consistent in the limit of the number of parallel replicates. This is appealing as the number of available processors increases much faster than clock speed, over recent years and for the years to come, for a number of reasons explained e.g. here.

## New R user community in Grenoble, France

Nine R user communities already exist in France and there is a much large number of R communities around the world. It was time for Grenoble to start its own!

The goal of the R user group is to facilitate the identification of local useRs, to initiate contacts, and to organise experience and knowledge sharing sessions. The group is open to any local useR interested in learning and sharing knowledge about R.

The group’s website features a map and table with members of the R group. Members with specific skills related to the use of R are referenced in a table and can be contacted by other members. A gitter allows members to discuss R issues and a calendar presents the upcoming events. (more…)

## Statistical learning in models made of modules

Hi,

With Lawrence Murray, Chris Holmes and Christian Robert, we have recently arXived a paper entitled “Better together? Statistical learning in models made of modules”. Christian blogged about it already. The context is the following: parameters of a first model appear as inputs in another model. The question is whether to consider a “joint model approach”, where all parameters are estimated simultaneously with all of the data. Or if one should instead follow a “modular approach”, where the first parameters are estimated with the first model only, ignoring the second model. Examples of modular approaches include the “cut distribution“, or “two-step estimators” (e.g. Chapter 6 of Newey & McFadden (1994)). In many fields, modular approaches are preferred, because the second model is suspected of being more misspecified than the first one. Misspecification of the second model can “contaminate” the joint model, with dire consequences on inference, as described e.g. in Bayarri, Berger & Liu (2009). Other reasons include computational constraints and the lack of simultaneous availability of all models and associated data. In the paper, we try to make sense of the defects of the joint model approach and we propose a principled, quantitative way of choosing between joint and modular approaches.

## School of Statistics for Astrophysics, Autrans, France, October 9-13

Didier Fraix-Burnet (IPAG), Stéphane Girard (Inria) and myself are organising a School of Statistics for Astrophysics, Stat4Astro, to be held in October in France. The primary goal of the School is to train astronomers to the use of modern statistical techniques. It also aims at bridging the gap between the two communities by emphasising on the practice during works in common, to give firm grounds to the theoretical lessons, and to initiate works on problems brought by the participants. There have been two previous sessions of this school, one on regression and one on clustering. The speakers of this edition, including Christian Robert, Roberto Trotta and David van Dyk, will focus on the** **Bayesian methodology, with the moral support of the Bayesian Society, ISBA. The interest of this statistical approach in astrophysics probably comes from its necessity and its success in determining the cosmological parameters from observations, especially from the cosmic background fluctuations. The cosmological community has thus been very active in this field (see for instance the Cosmostatistics Initiative COIN).

But the Bayesian methodology, complementary to the more classical frequentist one, has many applications in physics in general due to its faculty to incorporate a priori knowledge into the inference computation, such as the uncertainties brought by the observational processes.

As for sophisticated statistical techniques, astronomers are not familiar with Bayesian methodology in general, while it is becoming more and more widespread and useful in the literature. This school will form the participants to both a strong theoretical background and a solid practice of Bayesian inference:

- Introduction to R and Bayesian Statistics (Didier Fraix-Burnet, Institut de Planétologie et d’Astrophysique de Grenoble)
- Foundations of Bayesian Inference (David van Dyk, Imperial College London)
- Markov chain Monte Carlo (David van Dyk, Imperial College London)
- Model Building (David van Dyk, Imperial College London)
- Nested Sampling, Model Selection, and Bayesian Hierarchical Models (Roberto Trotta, Imperial College London)
- Approximate Bayesian Computation (Christian Robert, Univ. Paris-Dauphine, Univ. Warwick and Xi’an (!))
- Bayesian Nonparametric Approaches to Clustering (Julyan Arbel, Université Grenoble Alpes and Inria)

Feel free to register, we are not fully booked yet!

Julyan

## Sampling from a maximal coupling

Hi,

In a recent work on parallel computation for MCMC, and also in another one, and in fact also in an earlier one, my co-authors and I use a simple yet very powerful object that is standard in Probability but not so well-known in Statistics: the maximal coupling. Here I’ll describe what this is and an algorithm to sample from such couplings.

## Update on inference with Wasserstein distances

Hi again,

As described in an earlier post, Espen Bernton, Mathieu Gerber and Christian P. Robert and I are exploring Wasserstein distances for parameter inference in generative models. Generally, ABC and indirect inference are fun to play with, as they make the user think about useful distances between data sets (i.i.d. or not), which is sort of implicit in classical likelihood-based approaches. Thinking about distances between data sets can be a helpful and healthy exercise, even if not always necessary for inference. Viewing data sets as empirical distributions leads to considering the Wasserstein distance, and we try to demonstrate in the paper that it leads to an appealing inferential toolbox.

In passing, the first author Espen Bernton will be visiting Marco Cuturi, Christian Robert, Nicolas Chopin and others in Paris from September to January; get in touch with him if you’re over there!

We have just updated the arXiv version of the paper, and the main modifications are as follows.

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