Statistical inference from ill-known data using belief functions

Abstract

As a general formalism for uncertain reasoning, the theory of belief functions extends the logical and probabilistic approaches to uncertainty: A belief function (or a completely monotone Choquet capacity) can be seen both as a non additive measure and as a generalized set. In this paper, the theory of belief functions is argued to be a suitable framework for statistical analysis of low quality, i.e., imprecise and/or partially reliable data. After a reminder of general concepts of the theory, we show how this approach can be applied to statistical inference by viewing the normalized likelihood function as defining a consonant belief function. The links with likelihood-based and Bayesian inference are discussed.We then show how this method can be extended to the analysis of uncertain data. The approach is illustrated using a running example. © 2013 Springer-Verlag Berlin Heidelberg.