Introduction to Imprecise Probabilities

Chapter 16Computation

Matthias C. M. Troffaes¹ and Robert Hable²

¹Department of Mathematical Sciences, Durham University, UK

²Department of Mathematics, University of Bayreuth, Germany

16.1 Introduction

In this chapter, we will very briefly discuss the main aspects of implementing the practical calculations for inference and decision making. Specialized computational techniques for graphical models were discussed in Section 1.5.

We start with discussing computational aspects of the natural extension of a conditional lower prevision. Of course, when dealing with problems that involve imprecise probabilities, finding the natural extension is usually only part of the solution. Nevertheless, because the idea of natural extension is one of the core aspects of imprecise probability theory, it seems worth to spend at least a few pages on its computational aspects.

Next, we discuss the computational aspects of solving static decision problems.

What is discussed here draws mostly from the result presented in earlier chapters, particularly Chapters 2, 4, and 8.

For an implementation of the algorithms presented here, see for instance the Python library improb [627].

16.2 Natural extension

As we must be able to deal with finite domains for computations, we start this section with a discussion of conditional lower previsions on arbitrary domains. A general purpose algorithm for natural extension is then presented, followed by simpler and faster implementations for important special cases. ...