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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 in order to address more directly and efficiently the inference on the additional discrete-valued parameter and the assessment of its estimation uncertainty, possibly uncovering potential idiosyncratic drivers in the formation of preferences. We overcome initial difficulties in employing a standard Gibbs sampling strategy to approximate the posterior distribution of the EPL by combining the data augmentation procedure and the conjugacy of the Gamma prior distribution with a tuned joint Metropolis–Hastings algorithm within Gibbs. The effectiveness and usefulness of the proposal is illustrated with applications to simulated and real datasets.

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 Plackett-Luce model (PL) for ranked data assumes the forward order of the ranking process. This hypothesis postulates that the ranking process of the items is carried out by sequentially assigning the positions from the top (most liked) to the bottom (least liked) alternative. This assumption has been recently relaxed with the Extended Plackett-Luce model (EPL) through the introduction of the discrete reference order parameter, describing the rank attribution path. By starting from two formal properties of the EPL, the former related to the inverse ordering of the item probabilities at the first and last stage of the ranking process and the latter well-known as independence of irrelevant alternatives (or Luce's choice axiom), we derive novel diagnostic tools for testing the appropriateness of the EPL assumption as the actual sampling distribution of the observed rankings. These diagnostic tools can help uncovering possible idiosyncratic paths in the sequential choice process. Besides contributing to fill the gap of goodness-of-fit methods for the family of multistage models, we also show how one of the two statistics can be conveniently exploited to construct a heuristic method, that surrogates the maximum likelihood approach for inferring the underlying reference order parameter. The relative performance of the proposals, compared with more conventional approaches, is illustrated by means of extensive simulation studies.

Background Fusarium oxysporum f.sp. radicis-lycopersici (FORL) is one of the most destructive necrotrophic pathogens affecting tomato crops, causing considerable field and greenhouse yield losses. Despite such major economic impact, little is known about the molecular mechanisms regulating Fusarium oxysporum f.sp. radicis-lycopersici resistance in tomato. Results A transcriptomic experiment was carried out in order to investigate the main mechanisms of FORL response in resistant and susceptible isogenic tomato lines. Microarray analysis at 15 DPI (days post inoculum) revealed a distinct gene expression pattern between the two genotypes in the inoculated vs non-inoculated conditions. A model of plant response both for compatible and incompatible reactions was proposed. In particular, in the incompatible interaction an activation of defense genes related to secondary metabolite production and tryptophan metabolism was observed. Moreover, maintenance of the cell osmotic potential after the FORL challenging was mediated by a dehydration-induced protein. As for the compatible interaction, activation of an oxidative burst mediated by peroxidases and a cytochrome monooxygenase induced cell degeneration and necrosis. Conclusions Our work allowed comprehensive understanding of the molecular basis of the tomato-FORL interaction. The result obtained emphasizes a different transcriptional reaction between the resistant and the susceptible genotype to the FORL challenge. Our findings could lead to the improvement in disease control strategies. Electronic supplementary material The online version of this article (doi:10.1186/s12870-016-0740-5) contains supplementary material, which is available to authorized users.

Background The environment has a profound influence on the organoleptic quality of tomato (Solanum lycopersicum) fruit, the extent of which depends on a well-regulated and dynamic interplay among genes, metabolites and sensorial attributes. We used a systems biology approach to elucidate the complex interacting mechanisms regulating the plasticity of sensorial traits. To investigate environmentally challenged transcriptomic and metabolomic remodeling and evaluate the organoleptic consequences of such variations we grown three tomato varieties, Heinz 1706, whose genome was sequenced as reference and two ?local? ones, San Marzano and Vesuviano in two different locations of Campania region (Italy). Results Responses to environment were more pronounced in the two ?local? genotypes, rather than in the Heinz 1706. The overall genetic composition of each genotype, acting in trans, modulated the specific response to environment. Duplicated genes and transcription factors, establishing different number of network connections by gaining or losing links, play a dominant role in shaping organoleptic profile. The fundamental role of cell wall metabolism in tuning all the quality attributes, including the sensorial perception, was also highlighted. Conclusions Although similar fruit-related quality processes are activated in the same environment, different tomato genotypes follow distinct transcriptomic, metabolomic and sensorial trajectories depending on their own genetic makeup. Electronic supplementary material The online version of this article (doi:10.1186/s12870-017-1008-4) contains supplementary material, which is available to authorized users.

We propose the use of probability models for ranked data as a useful alternative to a quantitative data analysis to investigate the outcome of bioassay experiments, when the preliminary choice of an appropriate normalization method for the raw numerical responses is difficult or subject to criticism. We review standard distance-based and multistage ranking models and in this last context we propose an original generalization of the Plackett-Luce model to account for the order of the ranking elicitation process. The usefulness of the novel model is illustrated with its maximum likelihood estimation for a real data set. Specifically, we address the heterogeneous nature of experimental units via model-based clustering and detail the necessary steps for a successful likelihood maximization through a hybrid version of the Expectation-Maximization algorithm. The performance of the mixture model using the new distribution as mixture components is compared with those relative to alternative mixture models for random rankings. A discussion on the interpretation of the identified clusters and a comparison with more standard quantitative approaches are finally provided., (revised to properly include references)

In the context of capture–recapture experiments heterogeneous capture probabilities are often perceived as one of the most challenging features to be incorporated in statistical models. In this paper we propose within a Bayesian framework a new modeling strategy for inference on the unknown population size in the presence of heterogeneity of subject characteristics. Our approach is attractive in that parameters are easily interpretable. Moreover, no parametric distributional assumptions are imposed on the latent distribution of individual heterogeneous propensities to be captured. Bayesian inference based on marginal likelihood by-passes some common identifiability issues, and a formal default prior distribution can be derived. Alternative default prior choices are considered and compared. Performance of our formal default approach is favorably evaluated with two real data sets and with a small simulation study.

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.

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.

Since gene expression approaches constitute a starting point for investigating plant-pathogen systems, we performed a transcriptional analysis to identify a set of genes of interest in tomato plants infected with F. oxysporum f. sp. lycopersici (Fol) and Tomato Mosaic Virus (ToMV). Differentially expressed tomato genes upon inoculation with Fol and ToMV were identified at two days post-inoculation. A large overlap was found in differentially expressed genes throughout the two incompatible interactions. However, Gene Ontology enrichment analysis evidenced specific categories in both interactions. Response to ToMV seems more multifaceted, since more than 70 specific categories were enriched versus the 30 detected in Fol interaction. In particular, the virus stimulated the production of an invertase enzyme that is able to redirect the flux of carbohydrates, whereas Fol induced a homeostatic response to prevent the fungus from killing cells. Genomic mapping of transcripts suggested that specific genomic regions are involved in resistance response to pathogen. Coordinated machinery could play an important role in prompting the response, since 60% of pathogen receptor genes (NB-ARC-LRR, RLP, RLK) were differentially regulated during both interactions. Assessment of genomic gene expression patterns could help in building up models of mediated resistance responses.

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.

We developed a new phage-display based approach, the Large Fragment Phage Display (LFPD), that can be used for mapping conformational epitopes on target molecules of immunological interest. LFPD uses a simplified and more effective phage-display approach in which only a limited set of larger fragments (about 100 aa in length) are expressed on the phage surface. Using the human HER2 oncoprotein as a target, we identified novel B-cell conformational epitopes. The same homologous epitopes were also detected in rat HER2 and all corresponded to the epitopes predicted by computational analysis (PEPITO software), showing that LFPD gives reproducible and accurate results. Interestingly, these newly identified HER2 epitopes seem to be crucial for an effective immune response against HER2-overexpressing breast cancers and might help discriminating between metastatic breast cancer and early breast cancer patients. Overall, the results obtained in this study demonstrated the utility of LFPD and its potential application to the detection of conformational epitopes on many other molecules of interest, as well as, the development of new and potentially more effective B-cell conformational epitopes based vaccines.

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.

Peptide Microarray Immunoassay (PMI for brevity) is a novel technology that enables researchers to map a large number of proteomic measurements at a peptide level, providing information regarding the relationship between antibody response and clinical sensitivity. PMI studies aim at recognizing antigen-specific antibodies from serum samples and at detecting epitope regions of the protein antigen. PMI data present new challenges for statistical analysis mainly due to the structural dependence among peptides. A PMI is made of a complete library of consecutive peptides. They are synthesized by systematically shifting a window of a fixed number of amino acids through the finite sequence of amino acids of the antigen protein as ordered in the primary structure of the protein. This implies that consecutive peptides have a certain number of amino acids in common and hence are structurally dependent. We propose a new flexible Bayesian hierarchical model framework, which allows one to detect recognized peptides and bound epitope regions in a single framework, taking into account the structural dependence between peptides through a suitable latent Markov structure. The proposed model is illustrated using PMI data from a recent study about egg allergy. A simulation study shows that the proposed model is more powerful and robust in terms of epitope detection than simpler models overlooking some of the dependence structure. The Author 2011. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.2011 © The Author 2011. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

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.

Motivated by a real data set deriving from a study on the genetic determinants of the behavior of Mycobacterium tuberculosis (MTB) hosted in macrophage, we take advantage of the presence of control spots and illustrate modelling issues for background correction and the ensuing empirical findings resulting from a Bayesian hierarchical approach to the problem of detecting differentially expressed genes. We prove the usefulness of a fully integrated approach where background correction and normalization are embedded in a single model-based framework, creating a new tailored model to account for the peculiar features of DNA array data where null expressions are planned by design. We also advocate the use of an alternative normalization device resulting from a suitable reparameterization. The new model is validated by using both simulated and our MTB data. This work suggests that the presence of a substantial fraction of exact null expressions might be the effect of an imperfect background calibration and shows how this can be suitably re-calibrated with the information coming from control spots. The proposed idea can be extended to all experiments in which a subset of genes whose expression levels can be ascribed mainly to background noise is planned by design.

Estimation of rare event probability is a key issue of recent simulation literature. This topic is of major importance in queuing systems as well as extreme value analysis in many fields such as reliability, telecommunication and insurance risks. However, estimating rare events is a challenging problem from a methodological point of view: since, analytical computation of rare event probabilities can be achieved only for very simple distribution, Monte Carlo approximation have been proposed. In this paper, after a brief review of some recent literature, we propose an alternative method for estimating rare events using simulation: we propose a simple deterministic transform of the random sample drawn from the original distribution such that the rare events become not-so-rare. The new approach can be easily implemented and the resulting estimator can achieve a bounded relative error in some relevant cases such as exponential-like and regularly varying functions. The approach is presented here in a very simple basic setting of a single random variable but it can be also extended to sum of random variables.

Phylogenetics aims at inferring the tree that better represents the evolutionary relationships among species studying differences and similarities in DNA sequences in different taxonomies. Alternative estimation methods have been proposed from different perspectives (Gascuel, 2004, Swafford, 2003): in this work, we deal with a stochastic model for substitution rates estimating its parameters in a fully Bayesian framework. We focus on computational tools based on MCMC sampling. For a fixed topology we evaluate the evidence of two competing models through Bayes factor. Available computational tools are compared together with a new implementation of the generalized harmonic mean approach via hyperplane inflation recently proposed in Petris and Tardella (2007). When the topology is not known in advance, we will compare more conventional transdimensional MCMC sampler based on the reversible jump approach with the alternative geometric approach proposed in Petris and Tardella (2003).

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.