A Note on B-Splines for Semiparametric Elicitation

Abstract

In this article we introduce a novel method for transferring expert statements about an uncertain bounded quantity into a probability distribution. This is a challenging problem, as these statements are usually sparse and imprecise. We will approach both issues by penalization, such that the final distribution will contain the stated information, but subject to that distributes its probability mass as uniformly as possible. As a functional basis for the modeled distribution we use linear combinations of B-splines. B-splines are highly flexible, have excellent shape-preserving properties, and are also well suited for evaluation, differentiation, and integration.

An R-package implementing the methods described in this article is available as online supplemental material.

Keywords:  :

• Brier entropy
• Density estimation
• Expert information
• Quadratic programming