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

publication date

  • October 2015

start page

  • 2989

end page

  • 3001

issue

  • 15

volume

  • 85

international standard serial number (ISSN)

  • 0094-9655

electronic international standard serial number (EISSN)

  • 1563-5163

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.