## Applying Non-parametric Robust Bayesian Analysis to Non-Opinionated Judicial Neutrality

April, 1999

Tech Report

### Author(s)

Joseph B. Kadane, Elias Moreno, Maria Eglee Perez and Luis Raul Pericchi

### Abstract

This paper explores the usefulness of robust Bayesian analysis in the context of an applied problem, finding priors to model judicial neutrality in an age discrimination case. We seek large classes of prior distributions without trivial bounds on the posterior probability of a key set, that is, without bounds that are independent of the data. Such an exploration shows qualitatively where the prior elicitation matters most, and quantitatively how sensitive the conclusions are to specified prior changes. The novel non-parametric classes proposed and studied here represent judicial netrality and are reasonably wide so that when a clear conclusion emerges from the data at hand, this is arguably beyond a reasonable doubt.