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In this paper, we consider the problem of specifying priors for the variance components in the Bayesian analysis of the Besag-York-Mollié model, a model that is popular among epidemiologists for disease mapping. The model encompasses two sets of random effects: one spatially structured to model spatial autocorrelation and the other spatially unstructured to describe residual heterogeneity. In this model, prior specification for variance components is an important problem because these priors maintain their influence on the posterior distributions of relative risks when mapping rare diseases. We propose using generalised inverse Gaussian priors, a broad class of distributions that includes many distributions commonly used as priors in this context, such as inverse gammas. We discuss the prior parameter choice with the aim of balancing the prior weight of the two sets of random effects on total variation and controlling the amount of shrinkage. The suggested prior specification strategy is compared to popular alternatives using a simulation exercise and applications to real data sets.

In this article, various issues related to the implementation of the usual Bayesian Information Criterion (BIC) are critically examined in the context of modelling a finite population. A suitable design-based approximation to the BIC is proposed in order to avoid the derivation of the exact likelihood of the sample which is often very complex in a finite population sampling. The approximation is justified using a theoretical argument and a Monte Carlo simulation study.

With “ensemble properties” of small area estimators, we mean their ability to reproduce the Empirical Distribution Function (EDF) characterizing the collection of underlying small area parameters (means, totals). Good “ensemble properties” may be relevant when estimation of non-linear functionals of the EDF of small area parameters (such as their variance) is needed. Small area estimators associated to the popular Fay-Herriot model are considered. “Bayes estimators”, i.e. posterior means, do not enjoy of good ensemble properties. In this paper three different adjusted predictors are compared, by means of a simulation exercise, under the assumption of correctly specified model. As the distributional assumptions on the random effects are difficult to assess, the considered predictors are compared also with respect to their robustness to the presence of failures in the distributional assumptions on the random effects.

In this paper we introduce shrinkage estimators for the estimation of the Unemployment rate in small domains of the Italian Labour Force Survey. The proposed estimators are based on Hierarchical Linear Mixed Models and on the borrowing strength on both time series and cross section. Auxiliary information from source external to the Labour Force Survey is not considered. A Hierarchical Bayesian approach is adopted, in which models are solved by means of MCMC sampling algorithms. This allows to measure variability associated to estimators accounting, in a simple way, for all e uncertainty sources. Results highlight how, simple hierarchical models allows for remarkable gain in efficiency with respect to published estimates, and that models with a time series component perform better than those based exclusively on data from the same repetition of the survey.