 A Unified Framework for Bayesian and Non-Bayesian Decision Making and InferenceMathematics of Operations Research, 2022, vol. 47, issue 4, 2721-2742 Abstract: After showing, by means of a series of examples, that paradigms alternative to the Bayesian one obtain by simply replacing the notion of approximation associated with the latter, the paper presents a unified framework for theories of decision making and inference. Given a statistical model, the algebra of bounded random variables on the sample space is mapped homomorphically into an algebra of operators on a certain Hilbert space. Then, the choice of a norm or a divergence function on the latter algebra produces a theory of decision making and inference. Examples include models from the Choquet expected utility class, models from robust statistics, the smooth model, maxmin and maxmax (as limiting cases) as well as a novel theory. The paper also contributes to Bayesian theory, which obtains in correspondence to a Hilbert norm. It shows that Bayes’ theorem can be derived from the fundamental concept of conditional expectation and that it is the only updating rule for which the operations of updating and of calculating the predictive commute. Keywords: Primary: 91B06; secondary: 62A99; decision making; inference; statistical model; robust statistics; neo-Bayesian statistics; Bayes’ theorem; updating of capacities; axiomatic foundations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:4:p:2721-2742 Access Statistics for this article More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC. |
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