Anne Philippe

Nonparametric Convergence Assessment for MCMC Model Selection

This article considers the problem of assessing the performance of MCMC model selection algorithms using a variety of nonparametric techniques. We consider a wide range of model selection problems to which MCMC model selection may be applied and propose several distance measures that can be used to quantify the similarity between multiple replications. These measures may be used to assess convergence by examining how “close” these replications of the chain are, since if all chains are at stationarity, then this distance should be small. Finally, we describe an alternative approach based upon the estimation of the convergence rate of the sub-Markov chain represented by the model indicators and finish by illustrating our approaches with several practical examples.

Simulation of right and left truncated gamma distributions by mixtures

We study the properties of truncated gamma distributions and we derive simulation algorithms which dominate the standard algorithms for these distributions. For the right truncated gamma distribution, an optimal accept–reject algorithm is based on the fact that its density can be expressed as an infinite mixture of beta distribution. For integer values of the parameters, the density of the left truncated distributions can be rewritten as a mixture which can be easily generated. We give an optimal accept–reject algorithm for the other values of the parameter. We compare the efficiency of our algorithm with the previous method and show the improvement in terms of minimum acceptance probability. The algorithm proposed here has an acceptance probability which is superior to e/4.

A TEST FOR STATIONARITY VERSUS TRENDS AND UNIT ROOTS FOR A WIDE CLASS OF DEPENDENT ERRORS

We suggest a rescaled variance type of test for the null hypothesis of stationarity against deterministic and stochastic trends (unit roots). The deterministic trend can be represented as a general function in time (e.g., nonparametric, linear, or polynomial regression, abrupt changes in the mean). Under the null, the asymptotic distribution of the test is derived, and critical values are tabulated for a wide class of stationary processes with short, long, or negative dependence structure. A simulation study examines the performance of the test in terms of size and power. The empirical performance of the test is illustrated using the S&P 500 data.The authors thank the editor, the referees, and Karim Abadir for helpful comments and Alfredas RaA kauskas for drawing our attention to the criterion of Cremers and Kadelka (1986). The first authors work was supported by the ESRC grants R000238212 and R000239538. The last two authors were supported by a cooperation agreement CNRS/LITHUANIA (4714) and by a bilateral Lithuania-France research project Gilibert.

MCMC Control Spreadsheets for Exponential Mixture Estimation

Abstract This article presents Bayesian inference for exponential mixtures, including the choice of a noninformative prior based on a location-scale reparameterization of the mixture. Adapted control sheets are proposed for studying the convergence of the associated Gibbs sampler. They exhibit a strong lack of stability in the allocations of the observations to the different components of the mixture. The setup is extended to the case when the number of components in the mixture is unknown and a reversible jump MCMC technique is implemented. The results are illustrated on simulations and a real dataset.

Perfect simulation of positive Gaussian distributions

AbstractWe provide an exact simulation algorithm that produces variables from truncated Gaussian distributions on (

Statistical Inference and Monte Carlo Algorithms

\mathbb{R}

Time series aggregation, disaggregation and long memory ∗

+)p via a perfect sampling scheme, based on stochastic ordering and slice sampling, since accept-reject algorithms like the one of Geweke (1991) and Robert (1995) are difficult to extend to higher dimensions.

A two-sample test for comparison of long memory parameters

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motions with correlated components having different self-similarity indices.