Bayesian prior robustness using general $$\phi $$ ϕ -divergence measure

Bayesian robustness measure of classes of contaminated priors using general $$\phi $$ ϕ -divergence between two posterior distributions is introduced. Using the local curvature for the $$\phi $$ ϕ -divergence of the posterior distributions, we propose to extend the result of Dey and Birmiwal (1994), which consider the $$\epsilon $$ ϵ -contaminated and geometric mixing classes, to any prior contamination classes. Then, a new general explicit analytic formula for the local curvature is obtained. Moreover, we show that this curvature formula doesn’t depend on the contaminated posterior distribution and gives unified answers irrespective of the choice of the $$\phi $$ ϕ functions. As applications, both parametric and nonparametric prior contamination are considered.