Stochastic frontier models: a bayesian perspective

A Bayesian approach to estimation, prediction and model comparison in composed error production models is presented. A broad range of distributions on the inefficiency term define the contending models, which can either be treated separately or pooled. Posterior results are derived for the individual efficiencies as well as for the parameters, and the differences with the usual sampling-theory approach are highlighted. The required numerical integrations are handled by Monte Carlo methods with Importance Sampling, and an empirical example illustrates the procedures

On association in regression: the coefficient of determination revisited

Universal coefficients of determination are investigated which quantify the strength of the relation between a vector of dependent variables Y and a vector of independent covariates X. They are defined as measures of dependence between Y and X through theta(x), with theta(x) parameterizing the conditional distribution of Y given X=x. If theta(x) involves unknown coefficients gamma the definition is conditional on gamma, and in practice gamma, respectively the coefficient of determination has to be estimated. The estimates of quantities we propose generalize R^2 in classical linear regression and are also related to other definitions previously suggested. Our definitions apply to generalized regression models with arbitrary link functions as well as multivariate and nonparametric regression. The definition and use of the proposed coefficients of determination is illustrated for several regression problems with simulated and real data sets

Asymptotics for a Bayesian nonparametric estimator of species variety

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown that they can also be exploited in species sampling problems: indeed they are natural tools for modeling the random proportions of species within a population thus allowing for inference on various quantities of statistical interest. For applications that involve large samples, the exact evaluation of the corresponding estimators becomes impracticable and, therefore, asymptotic approximations are sought. In the present paper, we study the limiting behaviour of the number of new species to be observed from further sampling, conditional on observed data, assuming the observations are exchangeable and directed by a normalized generalized gamma process prior. Such an asymptotic study highlights a connection between the normalized generalized gamma process and the two-parameter Poisson-Dirichlet process that was previously known only in the unconditional case.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ371 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Sequential Empirical Bayes method for filtering dynamic spatiotemporal processes

We consider online prediction of a latent dynamic spatiotemporal process and estimation of the associated model parameters based on noisy data. The problem is motivated by the analysis of spatial data arriving in real-time and the current parameter estimates and predictions are updated using the new data at a fixed computational cost. Estimation and prediction is performed within an empirical Bayes framework with the aid of Markov chain Monte Carlo samples. Samples for the latent spatial field are generated using a sampling importance resampling algorithm with a skewed-normal proposal and for the temporal parameters using Gibbs sampling with their full conditionals written in terms of sufficient quantities which are updated online. The spatial range parameter is estimated by a novel online implementation of an empirical Bayes method, called herein sequential empirical Bayes method. A simulation study shows that our method gives similar results as an offline Bayesian method. We also find that the skewed-normal proposal improves over the traditional Gaussian proposal. The application of our method is demonstrated for online monitoring of radiation after the Fukushima nuclear accident