arXiv subjects

Cristiano Villa

Publications and source records attributed to Cristiano Villa.

23 records · Page 2Linked to original sources

arXiv2016

A Property of the Kullback--Leibler Divergence for Location-scale Models

In this paper, we discuss a property of the Kullback--Leibler divergence measured between two models of the family of the location-scale distributions. We show that, if model $M_1$ and model $M_2$ are represented by location-scale distributions, then the minimum Kullback--Leibler divergence from $M_1$ to $M_2$, with respect to the parameters of $M_2$, is independent from the value of the parameters of $M_1$. Furthermore, we show that the property holds for models that can be transformed into location-scale distributions. We illustrate a possible application of the property in objective Bayesian model selection.

math.ST↗

arXiv2016

Bayesian Estimation of the Threshold of a Generalised Pareto Distribution for Heavy-Tailed Observations

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 of a given set of observations. In other words, we assume that the threshold coincides to one of the data points. We show two ways of defining a prior: by assigning equal mass to each order statistic, that is a uniform prior, and by considering the worth that every order statistic has in representing the true threshold. Both proposed priors represent a scenario of minimal information, and we study their adequacy through simulation exercises and by analysing two applications from insurance and from finance.

stat.ME↗

arXiv2015

Model Prior Distribution for Variable Selection in Linear Regression Models

In this work we discuss a novel model prior probability for variable selection in linear regression. The idea is to determine the prior mass in an objective sense, by considering the worth of each of the possible regression models, given the number of covariates under consideration. Through a simulation study, we show that the proposed prior outperforms the uniform prior and the Scott \& Berger prior in a scenario of no prior knowledge about the size of the true regression models. We illustrate the use of the prior using two well-known data sets with, respectively, 15 and 4 covariates.

stat.ME↗

arXiv2015

On the Mathematics of the Jeffreys-Lindley Paradox

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 for the null hypothesis tends to one when the uncertainty, i.e. the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.

math.ST↗

arXiv2008

The invariant manifold approach applied to nonlinear dynamics of a rotor-bearing system

The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial condition. The procedure to determine the approximation of the invariant manifolds is discussed and a strategy to retain the speed dependent effects on the manifolds without solving the eigenvalue problem for each spin speed is presented. The performance of the reduced system is analysed in function of the spin speed.

physics.class-ph↗