On the Independence Jeffreys prior for skew--symmetric models with applications

We study the Jeffreys prior of the skewness parameter of a general class of scalar skew--symmetric models. It is shown that this prior is symmetric about 0, proper, and with tails $O(\lambda^{-3/2})$ under mild regularity conditions. We also calculate the independence Jeffreys prior for the case with unknown location and scale parameters. Sufficient conditions for the existence of the corresponding posterior distribution are investigated for the case when the sampling model belongs to the family of skew--symmetric scale mixtures of normal distributions. The usefulness of these results is illustrated using the skew--logistic model and two applications with real data

Approximate Bayesian conditional copulas

Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem, any multidimensional absolutely continuous distribution function can be uniquely represented as a copula, i.e. a joint cumulative distribution function on the unit hypercube with uniform marginals, which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the conditional copula, especially when one does not have enough information to select the copula model. Several Bayesian methods to approximate the posterior distribution of functionals of the dependence varying according covariates are presented and compared; the main advantage of the investigated methods is that they use nonparametric models, avoiding the selection of the copula, which is usually a delicate aspect of copula modelling. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics. (C) 2022 Elsevier B.V. All rights reserved

Generalized Bayesian Record Linkage and Regression with Exact Error Propagation

Record linkage (de-duplication or entity resolution) is the process of merging noisy databases to remove duplicate entities. While record linkage removes duplicate entities from such databases, the downstream task is any inferential, predictive, or post-linkage task on the linked data. One goal of the downstream task is obtaining a larger reference data set, allowing one to perform more accurate statistical analyses. In addition, there is inherent record linkage uncertainty passed to the downstream task. Motivated by the above, we propose a generalized Bayesian record linkage method and consider multiple regression analysis as the downstream task. Records are linked via a random partition model, which allows for a wide class to be considered. In addition, we jointly model the record linkage and downstream task, which allows one to account for the record linkage uncertainty exactly. Moreover, one is able to generate a feedback propagation mechanism of the information from the proposed Bayesian record linkage model into the downstream task. This feedback effect is essential to eliminate potential biases that can jeopardize resulting downstream task. We apply our methodology to multiple linear regression, and illustrate empirically that the "feedback effect" is able to improve the performance of record linkage.Comment: 18 pages, 5 figure

Robustezza bayesiana: tendenze attuali della ricerca

CIS

An Objective Bayesian Analysis of dichotomous sensitive data

We consider a dichotomous population in which every person belongs either to a sensitive group $A$ or to the non sensitive complement $\bar{A}$. The object of interest is to estimate the population proportion of individuals who are members of $A$. We refer to a randomized response model proposed by Huang (2004), where also another parameter is present, namely the probability that a respondent truthfully states that he/she belongs to $A$ in a direct response survey. In the paper the posterior distribution of the parameters under the joint Jeffreys and Reference prior is derived. The properties of the noninformative priors are investigated through the frequentist coverage probabilities of posterior quantiles

Approximate Bayesian methods for multivariate and conditional copulae

We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution, where copula is a flexible probabilistic tool that allows the researcher to model the joint distribution of a random vector in two separate steps: the marginal distributions and a copula function which captures the dependence structure among the vector components. The method is also based on the properties of an approximate BayesianMonteCarlo algorithm, where the proposed values of the functional of interest areweighted in terms of their empirical likelihood. This method is particularly useful when the likelihood function associated with theworking model is too costly to evaluate or when the working model is only partially specified