This paper describes a methodology that aims to enhance statistical inference in data envelopment analysis (DEA). In order to incorporate statistical properties in a DEA analysis we propose a combined application of a chance constrained DEA (CCDEA) model that is integrated with a stochastic mechanism from Bayesian techniques. The proposed method is conducted in two basic steps. In a first step we make use of Bayesian techniques on the data set to generate a statistical model and to simulate a large number of alternative data sets that can be observed as realizations. In a second step we solve the CCDEA problem for each and every one of the alternative samples, compute efficiency measures, and use the sampling distribution of these measures as an approximation to the finite sample distribution. The paper discusses the statistical advantages of this method using cross-sectional data from a sample of 117 Greek public hospitals. In testing the model we use homogeneous groups of hospitals in various sizes according to the hierarchical structure of the Greek health system (primary, secondary and tertiary care). In order to measure the overall technical efficiency of hospitals that are classified into different groups we introduce the concept of metafrontier analysis on the developed model. The results show that the tertiary and secondary hospitals operate with similar production technologies while a large technology gap is observed between the primary care hospitals and the metafrontier. 
Combining stochastic DEA with Bayesian analysis to obtain statistical properties of the efficiency scores: An application to Greek public hospitals