Heavy tailed priors: an alternative to non-informative priors in the estimation of proportions on small areas

TL;DR

This paper investigates heavy tailed priors, specifically Cauchy and Fuquene et al., as robust alternatives to non-informative priors for estimating small area proportions, demonstrating their effectiveness in survey sampling contexts.

Contribution

It introduces and evaluates heavy tailed priors, including a new one, for small area estimation, providing practical recommendations for their use in survey sampling.

Findings

Cauchy prior is recommended for outlier-robust estimation.

Fuquene et al. prior is suitable for specific small area outliers.

Heavy tailed priors improve robustness over traditional non-informative priors.

Abstract

We explore the Cauchy and a new heavy tailed (Fuquene, Perez and Pericchi (2011)) priors to estimate proportions on small areas. Hierarchical models and the Binomial likelihood in the exponential family form are used. We believe that the heavy tailed priors in survey sampling settings could be more effective than the choice of noninformative priors to eliminate antipathy towards methods that involve subjective elements or assumptions. To illustrate the robust Bayesian approach, we apply this methodology in a popular example: "the clement problem". Finally, we recommend to use the Cauchy prior in absence or presence of outliers within the small areas and the Fuquene et al. (2011) prior when the outlier is a particular small area.