BackgroundThe Human Microbiome has been variously associated with the immune-regulatory mechanisms involved in the prevention or development of many non-infectious human diseases such as autoimmunity, allergy and cancer. Integrative approaches which aim at associating the composition of the human microbiome with other available information, such as clinical covariates and environmental predictors, are paramount to develop a more complete understanding of the role of microbiome in disease development.ResultsIn this manuscript, we propose a Bayesian Dirichlet-Multinomial regression model which uses spike-and-slab priors for the selection of significant associations between a set of available covariates and taxa from a microbiome abundance table. The approach allows straightforward incorporation of the covariates through a log-linear regression parametrization of the parameters of the Dirichlet-Multinomial likelihood. Inference is conducted through a Markov Chain Monte Carlo algorithm, and selection of the significant covariates is based upon the assessment of posterior probabilities of inclusions and the thresholding of the Bayesian false discovery rate. We design a simulation study to evaluate the performance of the proposed method, and then apply our model on a publicly available dataset obtained from the Human Microbiome Project which associates taxa abundances with KEGG orthology pathways. The method is implemented in specifically developed R code, which has been made publicly available.ConclusionsOur method compares favorably in simulations to several recently proposed approaches for similarly structured data, in terms of increased accuracy and reduced false positive as well as false negative rates. In the application to the data from the Human Microbiome Project, a close evaluation of the biological significance of our findings confirms existing associations in the literature.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-017-1516-0) contains supplementary material, which is available to authorized users.

We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1's play and plays from the set {1, 2}. Both players win if Player 2's play equals Nature's play and lose otherwise. Players are told whether they have won or lost, and the game is repeated. An urn scheme for learning coordination in this game is as follows. Each node of the decision tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions. Players make decisions by drawing from the appropriate urns. After a win, each ball that was drawn is reinforced by adding another of the same color to the urn. A number of equilibria are possible for this game other than the optimal ones. However, we show that the urn scheme achieves asymptotically optimal coordination.

In this paper we propose a Bayesian nonparametric model for clustering grouped data. We adopt a hierarchical approach: at the highest level, each group of data is modeled according to a mixture, where the mixing distributions are conditionally independent normalized completely random measures (NormCRMs) centered on the same base measure, which is itself a NormCRM. The discreteness of the shared base measure implies that the processes at the data level share the same atoms. This desired feature allows to cluster together observations of different groups. We obtain a representation of the hierarchical clustering model by marginalizing with respect to the infinite dimensional NormCRMs. We investigate the properties of the clustering structure induced by the proposed model and provide theoretical results concerning the distribution of the number of clusters, within and between groups. Furthermore, we offer an interpretation in terms of generalized Chinese restaurant franchise process, which allows for posterior inference under both conjugate and non-conjugate models. We develop algorithms for fully Bayesian inference and assess performances by means of a simulation study and a real-data illustration. Supplementary Materials for this work is available online.

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Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling strategies together, by showing that a finite mixture is simply a realization of a point process. Following a Bayesian nonparametric perspective, we introduce a new class of prior: the Normalized Independent Point Processes. We investigate the probabilistic properties of this new class. Moreover, we design a conditional algorithm for finite mixture models with a random number of components overcoming the challenges associated with the Reversible Jump scheme and the recently proposed marginal algorithms. We illustrate our model on real data and discuss an important application in population genetics.

The great influence of uncertainties on the behavior of physical systems has always drawn attention to the importance of a stochastic approach to engineering problems. Accordingly, in this paper, we address the problem of solving a Finite Element analysis in the presence of uncertain parameters. We consider an approach in which several solutions of the problem are obtained in correspondence of parameters samples, and propose a novel non-intrusive method, which exploits the functional principal component analysis, to get acceptable computational efforts. Indeed, the proposed approach allows constructing an optimal basis of the solutions space and projecting the full Finite Element problem into a smaller space spanned by this basis. Even if solving the problem in this reduced space is computationally convenient, very good approximations are obtained by upper bounding the error between the full Finite Element solution and the reduced one. Finally, we assess the applicability of the proposed approach through different test cases, obtaining satisfactory results

This is the author's final version of the contribution published as:Argiento, R.; Guglielmi, A.; Lanzarone, E.; Nawajah, I. planning decisions related to service delivery in the territory must be taken. With the goal of helping home care management to take robust decisions, in this paper we propose a Bayesian model for estimating and predicting both the demand for care and the history of health conditions for patients in the charge of a home care service. In particular, we jointly model the temporal evolution of patients' care profile and the weekly number of visits required to nurses, and use a Markov chain Monte Carlo algorithm to compute posterior inference and prediction. The model is applied to data of one of the largest Italian home care providers, obtaining small prediction errors.

on the other. Here, two observations from the underlying species sampling mixture model share the same cluster if the distance between the densities corresponding to their latent parameters is smaller than a threshold. We complete this definition in order to define an equivalence relation among data labels. The resulting new random partition is coarser than the one induced by the species sampling mixture. Of course, since this procedure depends on the value of the threshold, we suggest a strategy to fix it. In addition, we discuss implementation and applications of the model to a simulated bivariate dataset from a mixture of two densities with a curved cluster, and to a dataset consisting of gene expression profiles measured at different times, known in literature as Yeast cell cycle data. Comparison with more standard clustering algorithm will be given. In both cases, the cluster estimates from our model turn out to be more effective. A primary application of our model is to the case of data from heavy tailed or curved clusters.