The Accelerated Central Cutting Plane Algorithm in the Numerical Treatment of Bayesian Global Prior Robustness Problems

• Activity Number: 203
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences*
• Author(s): Bruno Betro'*+
• Affiliation(s): CNR-IMATI
• Keywords: generalized moments ; robustness of Bayesian procedures ; linear semi-infinite programming ; numerical algorithms ; Bayesian analysis

Abstract

The problem of analyzing the robustness of Bayesian procedures with respect to the prior have been considered to some extent in the last years. In spite of this, robustness analysis has not yet entered into routine Bayesian analysis, mainly because of the inadequate development of numerical algorithms and related software. When the prior belongs to a class defined in terms of the so-called generalized moment conditions, it is well known that the problem reduces to one of Linear Semi-infinite Programming (LSIP). An algorithm for solving LSIP problems under mild assumptions on the functions defining the constraints, as required in global robustness by the typical presence of indicator functions, has been developed by the author. The algorithm, called Accelerated Central Cutting Plane (ACCP) algorithm, gives significant advantages in terms of speed of convergence over its ancestor, the well-known Central Cutting Plane algorithm. In this paper, after a brief review of the theory of global robustness under generalized moment condition and of the main features of the ACCP algorithm, the application of this latter to some global robustness problems is discussed through some examples.