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Cristiano Villa

Associate Professor of Mathematics at Duke Kunshan University
DKU Faculty

Selected Publications

Copula modelling with penalized complexity priors: the bivariate case

Journal Article Test · June 1, 2023 We explore the use of penalized complexity (PC) priors for assessing the dependence structure in a multivariate distribution F, with a particular emphasis on the bivariate case. We use the copula representation of F and derive the PC prior for the paramete ... Full text Cite

Bayesian Models Applied to Cyber Security Anomaly Detection Problems

Journal Article International Statistical Review · April 1, 2022 Cyber security is an important concern for all individuals, organisations and governments globally. Cyber attacks have become more sophisticated, frequent and dangerous than ever, and traditional anomaly detection methods have been proved to be less effect ... Full text Cite

An objective Bayes factor with improper priors

Journal Article Computational Statistics and Data Analysis · April 1, 2022 A new look at the use of improper priors in Bayes factors for model comparison is presented. As is well known, in such a case, the Bayes factor is only defined up to an arbitrary constant. Most current methods overcome the problem by using part of the samp ... Full text Cite

A loss-based prior for Gaussian graphical models

Journal Article Australian and New Zealand Journal of Statistics · December 1, 2020 Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool, which allows one to describe the relationships among the variables of interest. From the Bayesi ... Full text Cite

Loss-based approach to two-piece location-scale distributions with applications to dependent data

Journal Article Statistical Methods and Applications · June 1, 2020 Two-piece location-scale models are used for modeling data presenting departures from symmetry. In this paper, we propose an objective Bayesian methodology for the tail parameter of two particular distributions of the above family: the skewed exponential p ... Full text Cite

On a loss-based prior for the number of components in mixture models

Journal Article Statistics and Probability Letters · March 1, 2020 We introduce a prior distribution for the number of components of a mixture model. The prior considers the worth of each possible mixture, measured by a loss function with two components: one measures the loss in information in choosing the wrong mixture a ... Full text Cite

On a Class of Objective Priors from Scoring Rules (with Discussion)

Journal Article Bayesian Analysis · January 1, 2020 Objective prior distributions represent an important tool that allows one to have the advantages of using a Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off the chosen statis ... Full text Cite

A loss-based prior for variable selection in linear regression methods

Journal Article Bayesian Analysis · January 1, 2020 In this work we propose a novel model prior for variable selection in linear regression. The idea is to determine the prior mass by considering the worth of each of the regression models, given the number of possible covariates under consideration. The wor ... Full text Cite

Bayesian loss-based approach to change point analysis

Journal Article Computational Statistics and Data Analysis · January 1, 2019 A loss-based approach to change point analysis is proposed. In particular, the problem is looked from two perspectives. The first focuses on the definition of a prior when the number of change points is known a priori. The second contribution aims to estim ... Full text Cite

Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula

Journal Article Computational Statistics and Data Analysis · August 1, 2018 An objective Bayesian approach to estimate the number of degrees of freedom (ν) for the multivariate t distribution and for the t-copula, when the parameter is considered discrete, is proposed. Inference on this parameter has been problematic for the multi ... Full text Cite

Objective bayesian analysis of the Yule–Simon distribution with applications

Journal Article Computational Statistics · March 1, 2018 The Yule–Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, has ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule–Simon distribution. In p ... Full text Cite

On the mathematics of the Jeffreys–Lindley paradox

Journal Article Communications in Statistics - Theory and Methods · December 17, 2017 This paper is concerned with the well known Jeffreys–Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior fo ... Full text Cite

A note on the posterior inference for the Yule–Simon distribution

Journal Article Journal of Statistical Computation and Simulation · April 13, 2017 The Yule–Simon distribution has been out of the radar of the Bayesian community, so far. In this note, we propose an explicit Gibbs sampling scheme when a Gamma prior is chosen for the shape parameter. The performance of the algorithm is illustrated with s ... Full text Cite

Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations

Journal Article Test · March 1, 2017 In this paper, we discuss a method to define prior distributions for the threshold of a generalised Pareto distribution, in particular when its applications are directed to heavy-tailed data. We propose to assign prior probabilities to the order statistics ... Full text Cite

Objective Bayesian modelling of insurance risks with the skewed Student-t distribution

Journal Article Applied Stochastic Models in Business and Industry · March 1, 2017 Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these data sets. This work extends a methodology recently introduced in the literature by considering an extra parameter ... Full text Cite

An Objective Bayesian Criterion to Determine Model Prior Probabilities

Journal Article Scandinavian Journal of Statistics · December 1, 2015 We discuss the problem of selecting among alternative parametric models within the Bayesian framework. For model selection problems, which involve non-nested models, the common objective choice of a prior on the model space is the uniform distribution. The ... Full text Cite

An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces

Journal Article Journal of the American Statistical Association · July 3, 2015 We present a novel approach to constructing objective prior distributions for discrete parameter spaces. These types of parameter spaces are particularly problematic, as it appears that common objective procedures to design prior distributions are problem ... Full text Cite

Objective prior for the number of degrees of freedom of a t distribution

Journal Article Bayesian Analysis · January 1, 2014 In this paper, we construct an objective prior for the degrees of freedom of a t distribution, when the parameter is taken to be discrete. This parameter is typically problematic to estimate and a problem in objective Bayesian inference since improper prio ... Full text Cite