TY - JOUR

T1 - Optimal sequential testing for an inverse Gaussian process

AU - Buonaguidi, Bruno

AU - Muliere, Pietro

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Bayesian sequential testing

KW - Chebyshev polynomials

KW - Modeling and Simulation

KW - Statistics and Probability

KW - collocation method

KW - free-boundary problem

KW - inverse Gaussian process

KW - optimal stopping

KW - smooth and continuous fit principles

KW - Bayesian sequential testing

KW - Chebyshev polynomials

KW - Modeling and Simulation

KW - Statistics and Probability

KW - collocation method

KW - free-boundary problem

KW - inverse Gaussian process

KW - optimal stopping

KW - smooth and continuous fit principles

UR - http://hdl.handle.net/10807/133694

UR - http://www.tandf.co.uk/journals/titles/07474946.asp

U2 - 10.1080/07474946.2015.1099955

DO - 10.1080/07474946.2015.1099955

M3 - Article

VL - 35

SP - 69

EP - 83

JO - Sequential Analysis

JF - Sequential Analysis

SN - 0747-4946

ER -