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The PLMIX package offers a comprehensive framework aimed at endowing the R statistical environment with some recent methodological advances in modelling and clustering partially ranked data. The us...

The authors present theoretical results that show how one can simulate a mixture distribution whose components live in subspaces of different dimension by reformulating the problem in such a way that observations may be drawn from an auxiliary continuous distribution on the largest subspace and then transformed in an appropriate fashion. Motivated by the importance of enlarging the set of available Markov chain Monte Carlo (MCMC) techniques, the authors show how their results can be fruitfully employed in problems such as model selection (or averaging) of nested models, or regeneration of Markov chains for evaluating standard deviations of estimated expectations derived from MCMC simulations. Les auteurs presentent des resultats theoriques qui montrent comment il est possible de simuler un melange de lois dont les composantes vivent dans des sous-espaces de dimensions differentes en reformulant le probleme de sorte que les observations puissent ětre tirees d'une loi continue auxiliaire definie sur le plus grand sous-espace et ensuite transformees de facon appropriee. Motives par l'importance d'elargir l'eventail disponible de methodes de Monte-Carlo a chaǐne de Markov (MCCM), les auteurs montrent comment leurs resultats peuvent ětre mis a profit, entre autres, dans des situations de choix (ou de compromis) entre divers modeles emboǐtes ou de regeneration de chaǐnes de Markov pour l'evaluation de l'ecart type d'estimations d'esperances deduites de simulations par MCCM.

SUMMARY The intrinsic heterogeneity of individuals is a potential source of bias in estimation procedures for capture-recapture models. To account for this heterogeneity in the model a hierarchical structure has been proposed whereby the probabilities that each animal is caught on a single occasion are modelled as independent draws from a common unknown distribution F. However, there is general agreement that modelling F by a simple parametric curve may lead to unsatisfactory results. Here we propose an alternative Bayesian approach that relies on a different parameterisation which imposes no assumption on the shape of F but drives the problem back to a finite-dimensional setting. Our approach avoids some identifiability issues related to such a recapture model while allowing for a formal Bayesian default analysis. Results of analyses of computer simulations and of real data show that the method performs well.

The k-truncated moment class Γ( m k )={π∈ P : m i = ∫ I x i π( d x), i=1,…,k} of all probability distributions π on a compact interval I of the real line which have the same first k moments is considered. This paper derives some remarkable properties of the ranges of (k+h)th moments which allow to provide bounds for the diameter of Γ( m k ) for a suitable probability metric.

We explore the possibility of approximating the Ferguson-Dirichlet prior and the distributions of its random functionals through the simulation of random probability measures. The proposed procedure is based on the constructive definition illustrated in Sethuraman (1994) in conjunction with the use of a random stopping rule. This allows us to set in advance the closeness to the distributions of interest. The distribution of the stopping rule is derived, and the practicability of the simulating procedure is discussed. Sufficient conditions for convergence of random functionals are provided. The numerical applications provided just sketch the idea of the variety of nonparametric procedures that can be easily and safely implemented in a Bayesian setting.

We focus on a capture-recapture model in which capture prob- abilities arise from an unspecified distribution F. We show that model pa- rameters are identifiable based on the unconditional likelihood. This is not true with the conditional likelihood. We also clarify that consistency and asymptotic equivalence of maximum likelihood estimators based on condi- tional and unconditional likelihood do not hold. We show that estimates of the undetected fraction of population based on the unconditional likelihood converge to the so-called estimable sharpest lower bound and we derive a new asymptotic equivalence result. We finally provide theoretical and sim- ulation arguments in favor of the use of the unconditional likelihood rather than the conditional likelihood especially when one is willing to infer on the sharpest lower bound. AMS 2000 subject classifications: Primary 62G10; secondary 62F12.

Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake, and different approaches are used to compare them within a Bayesian framework. The Bayes factor, defined as the ratio of the marginal likelihoods of two competing models, plays a key role in Bayesian model selection. We focus on an alternative estimator of the marginal likelihood whose computation is still a challenging problem. Several computational solutions have been proposed, none of which can be considered outperforming the others simultaneously in terms of simplicity of implementation, computational burden and precision of the estimates. Practitioners and researchers, often led by available software, have privileged so far the simplicity of the harmonic mean (HM) estimator. However, it is known that the resulting estimates of the Bayesian evidence in favor of one model are biased and often inaccurate, up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful. We consider possible improvements of the generalized harmonic mean (GHM) idea that recycle Markov Chain Monte Carlo (MCMC) simulations from the posterior, share the computational simplicity of the original HM estimator, but, unlike it, overcome the infinite variance issue. We show reliability and comparative performance of the improved harmonic mean estimators comparing them to approximation techniques relying on improved variants of the thermodynamic integration.

We propose a robust model for discovering differentially expressed genes which directly incorporates biological significance, i.e., effect dimension. Using the so-called c-fold rule, we transform the expressions into a nominal observed random variable with three categories: below a fixed lower threshold, above a fixed upper threshold or within the two thresholds. Gene expression data is then transformed into a nominal variable with three levels possibly originated by three different distributions corresponding to under expressed, not differential, and over expressed genes. This leads to a statistical model for a 3-component mixture of trinomial distributions with suitable constraints on the parameter space. In order to obtain the MLE estimates, we show how to implement a constrained EM algorithm with a latent label for the corresponding component of each gene. Different strategies for a statistically significant gene discovery are discussed and compared. We illustrate the method on a little simulation study and a real dataset on multiple sclerosis.

An important goal of microarray studies is the detection of genes that show significant changes in observed expressions when two or more classes of biological samples such as treatment and control are compared. Using the c-fold rule, a gene is declared to be differentially expressed if its average expression level varies by more than a constant factor c between treatment and control (typically c=2). While often used, however, this simple rule is not completely convincing. By modeling this filter, a binary variable is defined at the genexexperiment level, allowing for a more powerful treatment of the corresponding information. A gene-specific random term is introduced to control for both dependence among genes and variability with respect to the c-fold threshold. Inference is carried out via a two-level finite mixture model under a likelihood approach. Then, parameter estimates are also derived using the counting distribution under a Bayesian nonparametric approach which allows to keep under control some error rate of erroneous discoveries. The effectiveness of both proposed approaches is illustrated through a large-scale simulation study and a well known benchmark data set.