Linearization of Bayesian robustness problems

One way to assess the dependence of the posterior on the choice of prior is to compute bounds of posterior expectations as the prior varies over a class of priors. We show how a simple linearization technique is useful for simplifying these computations in a wide variety of problems. This technique involves converting a single, nonlinear optimization into a set of linear optimizations. Our goal is to show the breadth and simplicity of the algorithm by showing how it may be applied in many situations. It has been suggested that Bayesian robustness problems may be built up sequentially, in the sense that constraints on the prior may be added one at a time, and the bounds on the posterior expectations may be examined at each stage. We will demonstrate that the linearization algorithm makes this approach tractable. We also show that approximating each step in the linearization algorithm can lead to accurate approximations to posterior bounds. © 1993.

Duke Scholars

Author Robert L. Wolpert Statistical Science