Bayesian analysis of ranking data with the constrained Extended Plackett-Luce model

Multistage ranking models, including the popular Plackett-Luce distribution (PL), rely on the assumption that the ranking process is performed sequentially, by assigning the positions from the top to the bottom one (forward order). A recent contribution to the ranking literature relaxed this assumption with the addition of the discrete-valued reference order parameter, yielding the novel Extended Plackett-Luce model (EPL). Inference on the EPL and its generalization into a finite mixture framework was originally addressed from the frequentist perspective. In this work, we propose the Bayesian estimation of the EPL with order constraints on the reference order parameter. The proposed restrictions reflect a meaningful rank assignment process. By combining the restrictions with the data augmentation strategy and the conjugacy of the Gamma prior distribution with the EPL, we facilitate the construction of a tuned joint Metropolis-Hastings algorithm within Gibbs sampling to simulate from the posterior distribution. The Bayesian approach allows to address more efficiently the inference on the additional discrete-valued parameter and the assessment of its estimation uncertainty. The usefulness of the proposal is illustrated with applications to simulated and real datasets.Comment: 20 pages, 4 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:1803.0288

An alternative marginal likelihood estimator for phylogenetic models

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 estimator (HM) and the arithmetic mean estimator (AM). 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. Our new implementation of the generalized harmonic mean (GHM) idea recycles MCMC simulations from the posterior, shares the computational simplicity of the original HM estimator, but, unlike it, overcomes the infinite variance issue. The alternative estimator is applied to simulated phylogenetic data and produces fully satisfactory results outperforming those simple estimators currently provided by most of the publicly available software

Bayesian Plackett--Luce Mixture Models for Partially Ranked Data

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

Indicatori AVA di ateneo: il contesto nazionale e Sapienza a confronto con i grandi atenei

Nell'ambito del sistema di Autovalutazione, Valutazione periodica e Accreditamento (AVA), rivolto alla valutazione periodica dei servizi didattici e all'accreditamento delle sedi e dei corsi di studio, l'ANVUR ha recentemente predisposto una serie di criteri e parametri nalizzati alla valutazione dell'ecienza accademica degli atenei italiani nei suoi molteplici aspetti. In questo articolo vengono analizzati i dati relativi alla prima rilevazione degli indicatori AVA di ateneo sulle cosiddette universita tradizionali (non telematiche). Oltre alla descrizione della variabilita che caratterizza il corpo delle universita italiane, l'analisi ore un inquadramento della performance di Sapienza Universita di Roma nel panorama accademico nazionale

ABC model choice via mixture weights estimation

I metodi di ABC (Approximate Bayesian Computation) sono largamente utilizzati per ottenere approssimazioni di distribuzioni a posteriori senza dover calcolare funzioni di verosimiglianza. Tuttavia, in generale, non e possibile trovare statistiche che siano sufficienti tra modelli e ciò rende poco attendibili gli strumenti classici su cui si basa l’ABC model choice. Al fine di superare tale problema, si propone di rimpiazzare il tradizionale confronto tra probabilità a posteriori dei modelli candidati con la stima a posteriori dei pesi di una mistura di tali modelli. Uno studio di simulazione mette in luce diversi punti di forza di questo approccio alternativo, presentandolo come una robusta e flessibile estensione di quello classico.Approximate Bayesian Computation (ABC) methods are widely employed to obtain approximations of posterior distributions without having to calculate likelihood functions. Nevertheless, the general impossibility to find statistics which are sufficient across models leads to unreliability of the classical tools for ABC model choice. To overcome this issue, a different kind of modelling is here proposed by replacing the traditional comparison between posterior probabilities of candidate models with posterior estimates of the weights of a mixture of these models. A simulation study highlights several strengths of this alternative approach, presenting it as a robust and flexible extension of the classical one

Efficient and accurate inference for mixtures of Mallows models with Spearman distance

The Mallows model occupies a central role in parametric modelling of ranking data to learn preferences of a population of judges. Despite the wide range of metrics for rankings that can be considered in the model specification, the choice is typically limited to the Kendall, Cayley or Hamming distances, due to the closed-form expression of the related model normalizing constant. This work instead focuses on the Mallows model with Spearman distance. An efficient and accurate EM algorithm for estimating finite mixtures of Mallows models with Spearman distance is developed, by relying on a twofold data augmentation strategy aimed at i) enlarging the applicability of Mallows models to samples drawn from heterogeneous populations; ii) dealing with partial rankings affected by diverse forms of censoring. Additionally, a novel approximation of the model normalizing constant is introduced to support the challenging model-based clustering of rankings with a large number of items. The inferential ability of the EM scheme and the effectiveness of the approximation are assessed by extensive simulation studies. Finally, we show that the application to three real-world datasets endorses our proposals also in the comparison with competing mixtures of ranking models.Comment: 20 pages, 6 Figures, 11 Table

Evidence of Facilitation Cascade Processes as Drivers of Successional Patterns of Ecosystem Engineers at the Upper Altitudinal Limit of the Dry Puna

Facilitation processes constitute basic elements of vegetation dynamics in harsh systems. Recent studies in tropical alpine environments demonstrated how pioneer plant species defined as "ecosystem engineers" are capable of enhancing landscape-level richness by adding new species to the community through the modification of microhabitats, and also provided hints about the alternation of different ecosystem engineers over time. Nevertheless, most of the existing works analysed different ecosystem engineers separately, without considering the interaction of different ecosystem engineers. Focusing on the altitudinal limit of Peruvian Dry Puna vegetation, we hypothesized that positive interactions structure plant communities by facilitation cascades involving different ecosystem engineers, determining the evolution of the microhabitat patches in terms of abiotic resources and beneficiary species hosted. To analyze successional mechanisms, we used a "space-for-time" substitution to account for changes over time, and analyzed data on soil texture, composition, and temperature, facilitated species and their interaction with nurse species, and surface area of engineered patches by means of chemical analyses, indicator species analysis, and rarefaction curves. A successional process, resulting from the dynamic interaction of different ecosystem engineers, which determined a progressive amelioration of soil conditions (e.g. nitrogen and organic matter content, and temperature), was the main driver of species assemblage at the community scale, enhancing species richness. Cushion plants act as pioneers, by starting the successional processes that continue with shrubs and tussocks. Tussock grasses have sometimes been found to be capable of creating microhabitat patches independently. The dynamics of species assemblage seem to follow the nested assemblage mechanism, in which the first foundation species to colonize a habitat provides a novel substrate for colonization by other foundation species through a facilitation cascade process