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In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…

In this paper reference and probability-matching priors are derived for the univariate Student $t$-distribution. These priors generally lead to procedures with properties frequentists can relate to while still retaining Bayes validity. The…

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…

The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a…

A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions --- say Gaussians --- as the prior distribution. When the updating takes place via a statistical model, one…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

In this paper, we present the Bayesian inference procedures for the parameters of the multivariate random effects model derived under the assumption of an elliptically contoured distribution when the Berger and Bernardo reference and the…

Autoregressive cokriging models have been widely used to emulate multiple computer models with different levels of fidelity. The dependence structures are modeled via Gaussian processes at each level of fidelity, where covariance structures…

Following the critical review of Seaman et al. (2012), we reflect on what is presumably the most essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian inference remains fairly stable under…

Inference and estimation are fundamental in statistics, system identification, and machine learning. When prior knowledge about the system is available, Bayesian analysis provides a natural framework for encoding it through a prior…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.

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.…

We propose a prior distribution for the number of components of a finite mixture model. The novelty is that the prior distribution is obtained by considering the loss one would incur if the true value representing the number of components…

The use of fossil evidence to calibrate divergence time estimation has a long history. More recently Bayesian MCMC has become the dominant method of divergence time estimation and fossil evidence has been re-interpreted as the specification…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

We perform a quantitative analysis of the gain/loss asymmetry for financial time series by using a Bayesian approach. In particular, we focus on some selected indices and analyze the statistical significance of the asymmetry amount through…

In this paper we present a loss-based approach to change point analysis. In particular, we look at the problem from two perspectives. The first focuses on the definition of a prior when the number of change points is known a priori. The…

Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these datasets. This work extends the methodology introduced in Villa and Walker (2014a) by considering…