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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 elicitation of an ordinal judgment on multiple alternatives is often required in many psychological and behavioral experiments to investigate preference/choice orientation of a specific population. The Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze rankings of a finite set of items. The present work introduces a Bayesian finite mixture of Plackett-Luce models to account for unobserved sample heterogeneity of partially ranked data. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and the derivation of existing maximum likelihood procedures as special instances of the proposed Bayesian method. Inference can be conducted with the combination of the Expectation-Maximization algorithm for maximum a posteriori estimation and the Gibbs sampling iterative procedure. We additionally investigate several Bayesian criteria for selecting the optimal mixture configuration and describe diagnostic tools for assessing the fitness of ranking distributions conditionally and unconditionally on the number of ranked items. The utility of the novel Bayesian parametric Plackett-Luce mixture for characterizing sample heterogeneity is illustrated with several applications to simulated and real preference ranked data. We compare our method with the frequentist approach and a Bayesian nonparametric mixture model both assuming the Plackett-Luce model as a mixture component. Our analysis on real datasets reveals the importance of an accurate diagnostic check for an appropriate in-depth understanding of the heterogenous nature of the partial ranking data.

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.

Summary. Motivated by the absolute risk predictions required in medical decision making and patient counseling, we propose an approach for the combined analysis of case-control and prospective studies of disease risk factors. The approach is hierarchical to account for parameter heterogeneity among studies and among sampling units of the same study. It is based on modeling the retrospective distribution of the covariates given the disease outcome, a strategy that greatly simplifies both the combination of prospective and retrospective studies and the computation of Bayesian predictions in the hierarchical casecontrol context. Retrospective modeling differentiates our approach from most current strategies for inference on risk factors, which are based on the assumption of a specific prospective model. To ensure modeling flexibility, we propose using a mixture model for the retrospective distributions of the covariates. This leads to a general nonlinear regression family for the implied prospective likelihood. After introducing and motivating our proposal, we present simple results that highlight its relationship with existing approaches, develop Markov chain Monte Carlo methods for inference and prediction, and present an illustration using ovarian cancer data.

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.

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.