The full Bayesian significance test (FBST) was introduced by Pereira and Stern for measuring the evidence of a precise null hypothesis. The FBST requires both numerical optimization and multidimensional integration, whose computational cost may be heavy when testing a precise null hypothesis on a scalar parameter of interest in the presence of a large number of nuisance parameters. In this paper we propose a higher order approximation of the measure of evidence for the FBST, based on tail area expansions of the marginal posterior of the parameter of interest. When in particular focus is on matching priors, further results are highlighted. Numerical illustrations are discussed.

Higher order asymptotic computation of Bayesian significance tests for precise null hypotheses in the presence of nuisance parameters

CABRAS, STEFANO;RACUGNO, WALTER;
2015

Abstract

The full Bayesian significance test (FBST) was introduced by Pereira and Stern for measuring the evidence of a precise null hypothesis. The FBST requires both numerical optimization and multidimensional integration, whose computational cost may be heavy when testing a precise null hypothesis on a scalar parameter of interest in the presence of a large number of nuisance parameters. In this paper we propose a higher order approximation of the measure of evidence for the FBST, based on tail area expansions of the marginal posterior of the parameter of interest. When in particular focus is on matching priors, further results are highlighted. Numerical illustrations are discussed.
Evidence; Highest probability density set; HOTA algorithm; Matching priors; Pereira and Stern procedure; Profile and modified profile likelihood root; Tail area approximation; Applied mathematics; Statistics and probability; Modeling and simulation; Statistics, probability and uncertainty
File in questo prodotto:
File Dimensione Formato  
2015-pereira-matching-jscs.pdf

embargo fino al 13/09/2019

Descrizione: Articolo principale
Tipologia: versione editoriale
Dimensione 1.38 MB
Formato Adobe PDF
1.38 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/181110
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact