Christian P. Robert

Deviance information criteria for missing data models

The deviance information criterion (DIC) introduced by Spiegelhalteret al. (2002) is directly inspired by linear and generalised linear models,but it is not so naturally de ned for missing data models. In this paper,we reassess the criterion for such models, testing the behaviour of variousextensions in the cases of mixture and random e ect models.

Inferring population history with DIY ABC

Summary: Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC. Availability: The software DIY ABC is freely available at http://www.montpellier.inra.fr/CBGP/diyabc. Contact: j.cornuet@imperial.ac.uk Supplementary information: Supplementary data are also available at http://www.montpellier.inra.fr/CBGP/diyabc

Computational and Inferential Difficulties with Mixture Posterior Distributions

Abstract This article deals with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of k! modes is known immediately. Standard Markov chain Monte Carlo (MCMC) techniques usually have difficulties with well-separated modes such as occur here; the MCMC sampler stays within a neighborhood of a local mode and fails to visit other equally important modes. We show that exploration of these modes can be imposed using tempered transitions. However, if the prior distribution does not distinguish between the different components, then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used. We propose alternatives for Bayesian inference for permutation invariant posteriors, including a clustering device and alternative appropriate loss functions.

An overview of robust Bayesian analysis

SummaryRobust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis.

Simulation of truncated normal variables

We provide simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with convex restricted parameter space for any covariance structure.

Approximate Bayesian Computational methods

Approximate Bayesian Computation (ABC) methods, also known as likelihood-free techniques, have appeared in the past ten years as the most satisfactory approach to intractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some degree from calibration difficulties that make them rather volatile in their implementation and thus render them suspicious to the users of more traditional Monte Carlo methods. In this survey, we study the various improvements and extensions brought on the original ABC algorithm in recent years.

Paleoclimatic record of a long deep sea core from the eastern Mediterranean

Abstract A deep-sea core over 16 m long from the crestal area of the Mediterranean Ridge has been investigated with different techniques, including quantitative micropaleontology, stable isotopes (measured on the epipelagic species Globigerinoides ruber and on the mesopelagic species Globorotalia inflata), and clay mineralogy. The resulting record of climatic fluctuations can be cross correlated to other Mediterranean cores by means of isochronous lithologies (tephra layers and sapropels). The climatic record of the Mediterranean is similar in character, phase, and chronology to the records investigated in the equatorial Pacific and in the Caribbean. Isotope stages 1 to 17 have been recognized. Cyclically repeated stagnant cycles resulting in sapropel deposition complicate both the isotopic and the faunal signal. The isotopic investigations reveal that the temperature change in the surface layers of the eastern Mediterranean was no greater than 8°C in the late “glacial” Pleistocene. The chronostratigraphic and biostratigraphic interpretation of Core KS09 indicate that the mean sedimentation rate was 2.4 cm/1000 years, a value very close to the 2.5 cm/1000 years calculated for the entire Quaternary section at DSDP Site 125, also located in the crestal area of the Mediterranean Ridge in the Ionian Basin. The base of KS09 is likely to be very close to the Brunhes/Matuyama boundary dated at 0.7 my.

Bayesian modelling and inference on mixtures of distributions

Publisher Summary Mixture distributions comprise a finite or infinite number of components, possibly of different distributional types, that can describe different features of data. The Bayesian paradigm allows for probability statements to be made directly about the unknown parameters, prior or expert opinion to be included in the analysis, and hierarchical descriptions of both local-scale and global features of the model. This chapter aims to introduce the prior modeling, estimation, and evaluation of mixture distributions in a Bayesian paradigm. The chapter shows that mixture distributions provide a flexible, parametric framework for statistical modeling and analysis. Focus is on the methods rather than advanced examples, in the hope that an understanding of the practical aspects of such modeling can be carried into many disciplines. It also points out the fundamental difficulty in doing inference with such objects, along with a discussion about prior modeling, which is more restrictive than usual, and the constructions of estimators, which also is more involved than the standard posterior mean solution. Finally, this chapter gives some pointers to the related models and problems like mixtures of regressions and hidden Markov models as well as Dirichlet priors.

The Bayesian choice : a decision-theoretic motivation

Contents: Introduction.- Decision-Theoretic Foundations of Statistical Inference.- From Prior Information to Prior Distributions.- Bayesian Point Estimation.- Tests and Confidence Regions.- Admissibility and Complete Classes.- Invariance, Haar Measures, and Equivariant Estimators.- Hierarchical and Empirical Bayes Extensions.- Bayesian Calculations.- A Defense of the Bayesian Choice.

Antarctic subtropical humid episode at the Paleocene-Eocene boundary: Clay-mineral evidence

Clay-mineral assemblages from East Antarctica have been analyzed at high stratigraphic resolution (20 to 1 ka) throughout the interval from 55.6 to 55.0 Ma, which includes the terminal Paleocene isotopic excursion in Ocean Drilling Program Site 690B on Maud Rise (lat 65°S) in the Weddell Sea region. Changes in the clay associations reflect a major increase in chemical weathering caused by increased temperature and/or rainfall in at least this sector of East Antarctica for a brief (270 ka) interval in the latest Paleocene. This represents the most intense warming known for the Cenozoic. This high-latitude climatic episode is recorded synchronously by stable isotopes and clay minerals. A progression is evident in the clay assemblages during the latest Paleocene that apparently reflects changing relations between temperature and precipitation. This sequence began with the interval of rapid temperature increase that marks the beginning of the oxygen isotopic excursion. A brief increase in kaolinite at the inception of the excursion suggests a temporary increase in year-round precipitation in Antarctica, in response to an increased continent-to-ocean temperature gradient. This kaolinite spike was followed by almost total dominance by smectite for the remainder of the isotopic excursion (∼120 ka), suggesting that warmer Southern Ocean surface temperatures of 18 to 22 °C were associated with seasonal precipitation (alternating wet and dry seasons). Claymineral variations on Antarctica during the isotopic excursion reflect a tight coupling between oceanic and continental climate change. Immediately following the excursion at ∼55.22 Ma, kaolinite percentages increased to values similar to modern subtropical-tropical areas for ∼150 ka, a remarkable event for the Antarctic. Abundant kaolinite suggests perennial rainfall and minimum soil temperatures of 15 °C during at least part of the year. The kaolinite increased during a time of lower Southern Ocean surface-water temperatures, suggesting increased atmospheric heat transport toward the poles. A temporary change in atmospheric circulation is suggested from dominantly zonal to meridional.