Optimal sequential testing for an inverse Gaussian process

Bruno Buonaguidi, Pietro Muliere

Risultato della ricerca: Contributo in rivistaArticolo in rivista

1 Citazioni (Scopus)

Abstract

ABSTRACT: We analyze the Bayesian formulation of the sequential testing of two simple hypotheses for the distributional characteristics of an inverse Gaussian process. This problem arises when we are willing to test the positive drift of an unobservable Brownian motion, for which only the first passage times over positive thresholds can be recorded. We show that the initial optimal stopping problem for the posterior probability of one of the hypotheses can be reduced to a free-boundary problem, whose unknown boundary points are characterized by the principles of the continuous or smooth fit and whose unknown value function solves a linear integro-differential equation over the continuation set. A numerical scheme, based on the collocation method for boundary value problems, is further illustrated, in order to get precise approximations of the free-boundary problem solution, which seems to be very hard to derive analytically, because of the particular structure of the Lévy measure of an inverse Gaussian process.
Lingua originaleEnglish
pagine (da-a)69-83
Numero di pagine15
RivistaSequential Analysis
Volume35
DOI
Stato di pubblicazionePubblicato - 2016

Keywords

  • Bayesian sequential testing
  • Chebyshev polynomials
  • Modeling and Simulation
  • Statistics and Probability
  • collocation method
  • free-boundary problem
  • inverse Gaussian process
  • optimal stopping
  • smooth and continuous fit principles

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