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Christian P. Robert

Publications and source records attributed to Christian P. Robert.

At least 73 records · Page 4Linked to original sources
arXiv2014

Reflecting about Selecting Noninformative Priors

Following the critical review of Seaman et al. (2012), we reflect on what is presumably the most essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian inference remains fairly stable under a large range of noninformative prior distributions. However, as discussed by \citet{Hd}, there may also be unintended consequences of a choice of a noninformative prior and, these authors consider this problem ignored in Bayesian studies. As they based their argumentation on four examples, we reassess these examples and their Bayesian processing via different prior choices. Our conclusion is to lower the degree of worry about the impact of the prior, exhibiting an overall stability of the posterior distributions. We thus consider that the warnings of Seaman et al. (2012), while commendable, do not jeopardize the use of most noninformative priors.

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arXiv2014

Accelerating Metropolis-Hastings algorithms: Delayed acceptance with prefetching

MCMC algorithms such as Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions as exemplified by huge datasets. We offer in this paper an approach to reduce the computational costs of such algorithms by a simple and universal divide-and-conquer strategy. The idea behind the generic acceleration is to divide the acceptance step into several parts, aiming at a major reduction in computing time that outranks the corresponding reduction in acceptance probability. The division decomposes the "prior x likelihood" term into a product such that some of its components are much cheaper to compute than others. Each of the components can be sequentially compared with a uniform variate, the first rejection signalling that the proposed value is considered no further, This approach can in turn be accelerated as part of a prefetching algorithm taking advantage of the parallel abilities of the computer at hand. We illustrate those accelerating features on a series of toy and realistic examples.

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arXiv2014

First moments of the truncated and absolute Student's variates

While some of the enclosed already is a well-known derivation, and the remaining may have been obtained in earlier publications, this note computes the first two moments of a Student's variate truncated at zero and of an absolute (or folded) Student's variate.

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arXiv2013

Bayesian Computational Tools

This chapter surveys advances in the field of Bayesian computation over the past twenty years, with missing data. It also contains some novel computational entries on the double-exponential model that may be of interest per se.

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arXiv2013

Efficient learning in ABC algorithms

Approximate Bayesian Computation has been successfully used in population genetics to bypass the calculation of the likelihood. These methods provide accurate estimates of the posterior distribution by comparing the observed dataset to a sample of datasets simulated from the model. Although parallelization is easily achieved, computation times for ensuring a suitable approximation quality of the posterior distribution are still high. To alleviate the computational burden, we propose an adaptive, sequential algorithm that runs faster than other ABC algorithms but maintains accuracy of the approximation. This proposal relies on the sequential Monte Carlo sampler of Del Moral et al. (2012) but is calibrated to reduce the number of simulations from the model. The paper concludes with numerical experiments on a toy example and on a population genetic study of Apis mellifera, where our algorithm was shown to be faster than traditional ABC schemes.

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arXiv2012

CosmoPMC: Cosmology Population Monte Carlo

We present the public release of the Bayesian sampling algorithm for cosmology, CosmoPMC (Cosmology Population Monte Carlo). CosmoPMC explores the parameter space of various cosmological probes, and also provides a robust estimate of the Bayesian evidence. CosmoPMC is based on an adaptive importance sampling method called Population Monte Carlo (PMC). Various cosmology likelihood modules are implemented, and new modules can be added easily. The importance-sampling algorithm is written in C, and fully parallelised using the Message Passing Interface (MPI). Due to very little overhead, the wall-clock time required for sampling scales approximately with the number of CPUs. The CosmoPMC package contains post-processing and plotting programs, and in addition a Monte-Carlo Markov chain (MCMC) algorithm. The sampling engine is implemented in the library pmclib, and can be used independently. The software is available for download at http://www.cosmopmc.info.

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arXiv2012

The anti-Bayesian moment and its passing

The present article is the reply to the discussion of our earlier "Not only defended but also applied" (arXiv:1006.5366, to appear in The American Statistician) that arose from our memory of a particularly intemperate anti-Bayesian statement in Feller's beautiful and classic book on probability theory. We felt that it was worth exploring the very extremeness of Feller's words, along with similar anti-Bayesian remarks by others, in order to better understand the background underlying controversies that still exist regarding the foundations of statistics. We thank the four discussants of our article for their contributions to our understanding of these controversies as they have existed in the past and persist today.

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arXiv2012

"Not only defended but also applied": The perceived absurdity of Bayesian inference

The missionary zeal of many Bayesians of old has been matched, in the other direction, by a view among some theoreticians that Bayesian methods are absurd-not merely misguided but obviously wrong in principle. We consider several examples, beginning with Feller's classic text on probability theory and continuing with more recent cases such as the perceived Bayesian nature of the so-called doomsday argument. We analyze in this note the intellectual background behind various misconceptions about Bayesian statistics, without aiming at a complete historical coverage of the reasons for this dismissal.

math.ST↗
arXiv2012

In praise of the referee

There has been a lively debate in many fields, including statistics and related applied fields such as psychology and biomedical research, on possible reforms of the scholarly publishing system. Currently, referees contribute so much to improve scientific papers, both directly through constructive criticism and indirectly through the threat of rejection. We discuss ways in which new approaches to journal publication could continue to make use of the valuable efforts of peer reviewers.

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arXiv2012

Reading Theorie Analytique des Probabilites

This note is an extended read of my read of Laplace's book Theorie Analytique des Probabilites, when considered from a Bayesian viewpoint but without historical nor comparative pretentions. A deeper analysis is provided in Dale (1999).

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arXiv2012

Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modeling

The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable support, as is nearly always the case in practice, it is generally quite difficult to get a handle on these spectra. We show that, if the augmentation space is finite, then (under regularity conditions) the operators defined by the DA and sandwich chains are compact, and the spectra are finite subsets of $[0,1)$. Moreover, we prove that the spectrum of the sandwich operator dominates the spectrum of the DA operator in the sense that the ordered elements of the former are all less than or equal to the corresponding elements of the latter. As a concrete example, we study a widely used DA algorithm for the exploration of posterior densities associated with Bayesian mixture models [J. Roy. Statist. Soc. Ser. B 56 (1994) 363--375]. In particular, we compare this mixture DA algorithm with an alternative algorithm proposed by Frühwirth-Schnatter [J. Amer. Statist. Assoc. 96 (2001) 194--209] that is based on random label switching.

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arXiv2011

Regularization in regression: comparing Bayesian and frequentist methods in a poorly informative situation

Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and real datasets. This comparison includes new global noninformative approaches for Bayesian variable selection built on Zellner's g-priors that are similar to Liang et al. (2008). The interest of those calibration-free proposals is discussed. The numerical experiments we present highlight the appeal of Bayesian regularization methods, when compared with non-Bayesian alternatives. They dominate frequentist methods in the sense that they provide smaller prediction errors while selecting the most relevant variables in a parsimonious way.

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arXiv2011

Inherent Difficulties of Non-Bayesian Likelihood-based Inference, as Revealed by an Examination of a Recent Book by Aitkin

For many decades, statisticians have made attempts to prepare the Bayesian omelette without breaking the Bayesian eggs; that is, to obtain probabilistic likelihood-based inferences without relying on informative prior distributions. A recent example is Murray Aitkin's recent book, {\em Statistical Inference}, which presents an approach to statistical hypothesis testing based on comparisons of posterior distributions of likelihoods under competing models. Aitkin develops and illustrates his method using some simple examples of inference from iid data and two-way tests of independence. We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective and why we do not find it relevant for applied work.

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