Saddlepoint approximations for the Bingham and Fisher-Bingham normalising constants

Kume, Alfred and Wood, Andrew T.A. (2005) Saddlepoint approximations for the Bingham and Fisher-Bingham normalising constants. Biometrika, 92 (2). pp. 465-476. ISSN 0006-3444. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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The Fisher-Bingham distribution is obtained when a multivariate normal random vector is conditioned to have unit length. Its normalising constant can be expressed as an elementary function multiplied by the density, evaluated at 1, of a linear combination of independent noncentral chi(1)(2) random variables. Hence we may approximate the normalising constant by applying a saddlepoint approximation to this density. Three such approximations, implementation of each of which is straightforward, are investigated: the first-order saddlepoint density approximation, the second-order saddlepoint density approximation and a variant of the second-order approximation which has proved slightly more accurate than the other two. The numerical and theoretical results we present show that this approach provides highly accurate approximations in a broad spectrum of cases.

Item Type: Article
Uncontrolled keywords: complex Bingham distribution; directional data; shape analysis; von Mises-fisher distribution; Watson distribution
Subjects: H Social Sciences > HA Statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:19
Last Modified: 04 Jul 2014 15:54
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