Computation
Matthias C. M. Troffaes, Robert Hable · Wiley series in probability and statistics · 2014
This chapter discusses the main aspects of implementing the practical calculations for inference and decision making. It starts by explaining the computational aspects of the natural extension of a conditional lower prevision. When dealing with problems that involve imprecise probabilities, finding the natural extension is usually only part of the solution. But since the idea of natural extension is one of the core aspects of imprecise probability theory, computational aspects of natural extension are briefly discussed in the chapter. The chapter also explains the computational aspects of solving static decision problems. It presents the Walley, Pelessoni and Vicig algorithm for finding the natural extension, by means of a sequence of linear programs. The algorithm performs best if the gambles are sorted in advance, for instance by lower or upper prevision using a quick approximate version of the natural extension, such as Choquet integration or linear-vacuous approximation.