A Note on B-Splines for Semiparametric Elicitation

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 d...

Full description

Saved in:
Bibliographic Details
Published inThe American statistician Vol. 63; no. 4; pp. 373 - 377
Main Authors Bornkamp, Björn, Ickstadt, Katja
Format Journal Article
LanguageEnglish
Published Alexandria, VA Taylor & Francis 01.11.2009
American Statistical Association
Subjects
Approximations and expansions
Brier entropy
Density estimation
Distribution functions
Distribution theory
Drug design
Entropy
Estimating techniques
Exact sciences and technology
Expert information
General topics
Knots
Mathematical analysis
Mathematics
Modeling
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Polygons
Probabilities
Probability and statistics
Probability distribution
Probability distributions
Probability theory and stochastic processes
Quadratic programming
Quantiles
Sciences and techniques of general use
Statistical analysis
Statistical methods
Statistics
B spline
Density estimation
Integration
Probability
Probability distribution
Semiparametric method
Quadratic programming
Statistics
Linear model
Spline approximation
Numerical approximation
Functional
Linear combination
Expert information
Distribution function
Brier entropy
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0003-1305
1537-2731
DOI:10.1198/tast.2009.08191