Cristiano Villa

Objective Prior for the Number of Degrees of Freedom of a t Distribution

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 priors lead to improper posteriors, whilst proper priors may dom- inate the data likelihood. We nd an objective criterion, based on loss functions, instead of trying to dene objective probabilities directly. Truncating the prior on the degrees of freedom is necessary, as the t distribution, above a certain number of degrees of freedom, becomes the normal distribution. The dened prior is tested in simulation scenarios, including linear regression with t-distributed errors, and on real data: the daily returns of the closing Dow Jones index over a period of 98 days.

An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces

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 specific. We propose an objective criterion, based on loss functions, instead of trying to define objective probabilities directly. We systematically apply this criterion to a series of discrete scenarios, previously considered in the literature, and compare the priors. The proposed approach applies to any discrete parameter space, making it appealing as it does not involve different concepts according to the model. Supplementary materials for this article are available online.

A Note on the Posterior Inference for the Yule-Simon Distribution

ABSTRACT 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 simulation studies, including count data regression, and a real data application to text analysis. We compare our proposal to the frequentist counterparts showing better performance of our algorithm when a small sample size is considered.

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

An objective Bayesian approach to estimate the number of degrees of freedom

Objective bayesian analysis of the Yule–Simon distribution with applications

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On the mathematics of the Jeffreys–Lindley paradox

for the multivariate

Bayesian loss-based approach to change point analysis

t

An Objective Bayesian Criterion to Determine Model Prior Probabilities

distribution and for the

Objective Bayesian modelling of insurance risks with the skewed Student-tdistribution: F. LEISEN, J. MIGUEL MARIN AND C. VILLA

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On a Global Objective Prior from Score Rules

-copula, when the parameter is considered discrete, is proposed. Inference on this parameter has been problematic for the multivariate