On a class of prior distributions that accounts for uncertainty in the data

Abstract

A new class of prior distributions that can be used to assess the sensitivity of the Bayesian posterior inference to uncertainty in the data is proposed. This class is derived starting from an initial prior distribution and the likelihood function. We establish the mathematical properties of this class and the conditions under which ordering can be established within this class. We show how the sensitivity analysis can be performed using a standard MCMC procedure for any model whose likelihood, or an approximation, is available in a closed form and illustrate using examples. We also discuss how the proposed class is connected to the main ideas behind the Approximate Bayesian Computation (ABC) method. For this reason, we choose to call the new class of prior distributions as the ABC class of prior distributions. Finally, we close by sketching further possible extensions to this work.