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dc.contributor.authorTaraldsen, Gunnar
dc.contributor.authorTufto, Jarle
dc.contributor.authorLindqvist, Bo Henry
dc.date.accessioned2022-03-11T07:15:35Z
dc.date.available2022-03-11T07:15:35Z
dc.date.created2021-11-02T18:50:24Z
dc.date.issued2021
dc.identifier.citationScandinavian Journal of Statistics. 2021, .en_US
dc.identifier.issn0303-6898
dc.identifier.urihttps://hdl.handle.net/11250/2984409
dc.description.abstractWhat is a good prior? Actual prior knowledge should be used, but for complex models this is often not easily available. The knowledge can be in the form of symmetry assumptions, and then the choice will typically be an improper prior. Also more generally, it is quite common to choose improper priors. Motivated by this we consider a theoretical framework for statistics that includes both improper priors and improper posteriors. Knowledge is then represented by a possibly unbounded measure with interpretation as explained by Rényi in 1955. The main mathematical result here is a constructive proof of existence of a transformation from prior to posterior knowledge. The posterior always exists and is uniquely defined by the prior, the observed data, and the statistical model. The transformation is, as it should be, an extension of conventional Bayesian inference as defined by the axioms of Kolmogorov. It is an extension since the novel construction is valid also when replacing the axioms of Kolmogorov by the axioms of Rényi for a conditional probability space. A concrete case based on Markov Chain Monte Carlo simulations and data for different species of tropical butterflies illustrate that an improper posterior may appear naturally and is useful. The theory is also exemplified by more elementary examples.en_US
dc.language.isoengen_US
dc.publisherWileyen_US
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.no*
dc.titleImproper priors and improper posteriorsen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.description.versionpublishedVersionen_US
dc.source.pagenumber0en_US
dc.source.journalScandinavian Journal of Statisticsen_US
dc.identifier.doi10.1111/sjos.12550
dc.identifier.cristin1950763
cristin.ispublishedtrue
cristin.fulltextoriginal
cristin.qualitycode2


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Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal
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