A Note on Bayesian Model Selection for Discrete Data Using Proper Scoring Rules

We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal likelihood function in such a case, we apply a homogeneous scoring rule. For the particular case of distinguishing between Poisson and Negative Binomial models, we conduct simulations that indicate that, applied prequentially, the method will consistently select the true model.Comment: 8 pages, 2 figure

Properties of given and detected unbounded solutions to a class of chemotaxis models

This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction-repulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect Lebesgue spaces where given unbounded solutions blow-up also in the corresponding norms of those spaces; subsequently, estimates for the blow-up time are established. Finally, for a simplified version of the model, some blow-up criteria are proved

Modeling sign concordance of quantile regression residuals with multiple outcomes

Quantile regression permits describing how quantiles of a scalar response vari- able depend on a set of predictors. Because a unique de nition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is somewhat complicated. In this paper, we describe a simple approach based on a two-step procedure: in the  rst step, quantile regression is applied to each re- sponse separately; in the second step, the joint distribution of the signs of the residuals is modeled through multinomial regression. The described approach does not require a multidimensional de nition of quantiles, and can be used to capture important features of a multivariate response and assess the e ects of co- variates on the correlation structure. We apply the proposed method to analyze two di erent datasets

Parametric modeling of dependence of bivariate quantile regression residuals' signs

In this thesis, we propose a non-parametric method to study the dependence of the quantiles of a multivariate response conditional on a set of covariates. We define a statistic that measures the conditional probability of concordance of the signs of the residuals of the conditional quantiles of each univariate response. The probability of concordance is bounded from below by the value of largest possible negative dependence and from above by that of largest possible positive dependence. The value corresponding to the case of independence is contained in the interior of that interval. We recommend two distinct regression methods to model the conditional probability of concordance. The first is a logistic regression with a logit link modified. The second one is a nonlinear regression method, where the outcome is modeled as a polynomial function of the linear predictor. Both are conceived to constrain the predicted probabilities to lie within the feasible range. The estimated probabilities can be tested against the values of largest possible dependence and independence. The method permits to capture important aspects of the dependence of multivariate responses and assess possible effects of covariates on such dependence. We use data on pulmonary disfunctions to illustrate the potential of the proposed method. We suggest also graphical tools for a correct interpretation of results

Testing the equality of two coefficients of variation: a new Bayesian approach

The use of testing procedures for comparing two coefficients of variation (CVs) of independent populations is not extensively explored in the Bayesian context. We propose to address this issue through a test based on a measure of evidence, the Bayesian Discrepancy Measure, recently introduced in the literature. Computing the Bayesian Discrepancy Measure is straightforward when the CVs depend on a single parameter of the distribution. In contrast, it becomes more difficult when this simplification does not occur since more parameters are involved, requiring often the use of MCMC methods. We derive the Bayesian Discrepancy Measure and the related test by considering a variety of distribution assumptions with multiparametric CVs and apply them to real datasets. As far as we know, some of the examined problems have not yet been covered in the literature

Comparing the safety of COVID-19 vaccines: a geometrical approach

The prompt development of multiple vaccines for the immunization against the world-wide spread of the COVID-19 infection has raised the issue of comparison of their efficacy and of symptomatic effects on the population treated. The different trial reports, made available from the vaccine producers and from the regulatory authorities, analyze some selected systemic reactions reported from patients after the doses received, these are given in a graded scale. In this contribute we propose a geometric way to compare frequency distributions of categorical variables by introducing a distance measure from the best possible scenario in this repartition. The measure proposed is suitable for a direct comparison among the vaccines in terms of the severity of symptomatic reactions

A scientometric analysis of the effect of COVID-19 on the spread of research outputs

The spread of the COVID-19 pandemic in 2020 had a huge impact on the life course of all of us. This rapid spread has also caused an increase in the research production in topics related to different aspects of COVID-19. Italy has been one of the first countries to be massively involved in the outbreak of the disease. In this paper, we present an extensive scientometric analysis of the research production both at global (entire literature produced in the first 2 years after the beginning of the pandemic) and local level (COVID-19 literature produced by authors with an Italian affiliation). Our results showed that US and China are the most active countries in terms of number of publications and that the number of collaborations between institutions varies depending on geographical distance. Moreover, we identified the medical-biological as the field with the greatest growth in terms of literature production. As regards the analysis focused on Italy, we have shown that most of the collaborations follow a geographical pattern, both externally (with a preference for European countries) and internally (two clusters of institutions, north versus center-south). Furthermore, we explored the relationship between the number of citations and variables obtained from the data set (e.g. number of authors). Using multiple correspondence analysis and quantile regression we shed light on the role of journal topics and impact factor, the type of article, the field of study and how these elements affect citations

A multilevel Analysis of University attractiveness in the network flows from Bachelor to Master’s degree

In this work we aim to study the mobility choices of Italian students in the transition from bachelor to masters degree in order to assess the role played by the field of study. We consider micro-data from the Italian National Student Archive on a cohort of students enrolled for the first time at the university in a.y. 2011-12 who enrolled to a master degree program in the a.y. 2014-15 or 2015-16. We study the incoming and outgoing flows of students moving from bachelor to master’s degree between provinces and universities. We then assess the effects on mover choices of network centrality measures in terms of hub and authorities adopting a multilevel multinomial logit model

Logistic quantile regression to model cognitive impairment in Sardinian cancer patients

When analyzing outcome variables that take on values within a finite bounded interval, standard analyses are often inappropriate. The conditional distribution of bounded outcomes given covariates is often asymmetric and bimodal (e.g., J- or U-shaped) and may substantially vary across covariate patterns. Analyzing this type of outcomes calls for specific methods that can constrain inference within the feasible range. The conditional mean is generally not an effective summary measure of a bounded outcome, and conditional quantiles are preferable. In this chapter we present an application of logistic quantile regression to model the relationship between Mini Mental State Examination (MMSE), a cognitive impairment score bounded between 0 and 30, with age and the results of a biochemical analysis (Oil Red O) for the determination of cytoplasmic neutral lipids in peripheral blood mononuclear cells in a sample of 124 cancer patients living in Sardinia, Italy. In addition we discuss an internal cross-validation method to optimally select the boundary correction in the logit transform

A Bayesian Test for the comparison of two independent populations

In this paper, we propose a testing procedure that allows to compare pa- rameter functions from two independent populations. We address this issue through a test based on the Bayesian Discrepancy Measure, a measure of evidence recently introduced in the literature. This approach is flexible, as it can be adapted to take into account different distributions and different parameter transformations. In ad- dition, this methodology enables us to tackle problems that are not yet covered in the literature