Bayesian empirical likelihood inference with complex survey data

Evaluation of spatial Bayesian Empirical Likelihood models in analysis of small area data

Bayesian empirical likelihood (BEL) models are becoming increasingly popular as an attractive alternative to fully parametric models. However, they have only recently been applied to spatial data analysis for small area estimation. This study considers the development of spatial BEL models using two popular conditional autoregressive (CAR) priors, namely BYM and Leroux priors. The performance of the proposed models is compared with their parametric counterparts and with existing spatial BEL models using independent Gaussian priors and generalised Moran basis priors. The models are applied to two benchmark spatial datasets, simulation study and COVID-19 data. The results indicate promising opportunities for these models to capture new insights into spatial data. Specifically, the spatial BEL models outperform the parametric spatial models when the underlying distributional assumptions of data appear to be violated.

A unified Bayesian framework for exact inference of area under the receiver operating characteristic curve

The area under the receiver operating characteristic curve is a widely used measure for evaluating the performance of a diagnostic test. Common approaches for inference on area under the receiver operating characteristic curve are usually based upon approximation. For example, the normal approximation based inference tends to suffer from the problem of low accuracy for small sample size. Frequentist empirical likelihood based approaches for area under the receiver operating characteristic curve estimation may perform better, but are usually conducted through approximation in order to reduce the computational burden, thus the inference is not exact. By contrast, we proposed an exact inferential procedure by adapting the empirical likelihood into a Bayesian framework and draw inference from the posterior samples of the area under the receiver operating characteristic curve obtained via a Gibbs sampler. The full conditional distributions within the Gibbs sampler only involve empirical likelihoods with linear constraints, which greatly simplify the computation. To further enhance the applicability and flexibility of the Bayesian empirical likelihood, we extend our method to the estimation of partial area under the receiver operating characteristic curve, comparison of multiple tests, and the doubly robust estimation of area under the receiver operating characteristic curve in the presence of missing test results. Simulation studies confirm the desirable performance of the proposed methods, and a real application is presented to illustrate its usefulness.