Linearization of Bayesian Robustness Problems

Michael Lavine, Larry Wasserman, Robert Wolpert
Duke University, Carnegie Mellon University

Nov 30 1990

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, non-linear optimization into a set of linear optimization. Our goal is to show the breadth and simplicity of the algorithm by showing how it may be applies 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 approximately each step in the linearization algorithm can lead to accurate approximations to posterior bounds.


Bayesian robustness, linearization, upper and lower probabilities


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