Asymptotic Expansions for the Bingham Distribution

Kent, John T.

doi:10.2307/2347545

Cited by 21 publications

(8 citation statements)

References 12 publications

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“…Although a maximum likelihood estimator for A can be derived by iterative techniques which are based on being able to approximate c(A) (see, for example, Kent;2005, 2007Sei and Kume;2013), very little attention has been drawn in the literature concerning estimation of A within a Bayesian framework. Walker (2013) considered Bayesian inference for the Bingham distribution which removes the need to compute the normalising constant, using a (more general) method that was developed earlier 2011) and cleverly gets around the intractable nature of the normalising constant.…”

Section: Introductionmentioning

confidence: 99%

Exact Bayesian inference for the Bingham distribution

Fallaize

Kypraios

2014

Stat Comput

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This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameterdependent normalising constant of the Bingham distribution, which, even when it can be evaluated or accurately approximated, would have to be calculated at each iteration of an MCMC scheme, thereby greatly increasing the computational burden. We propose a method which enables exact (in Monte Carlo sense) Bayesian inference for the unknown parameters of the Bingham distribution by completely avoiding the need to evaluate this constant. We apply the method to simulated and real data, and illustrate that it is simpler to implement, faster, and performs better than an alternative algorithm that has recently been proposed in the literature.

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Section: Introductionmentioning

confidence: 99%

Exact Bayesian inference for the Bingham distribution

Fallaize

Kypraios

2014

Stat Comput

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“…Typically, this is done via series expansion [3], [12], although saddle-point approximations [13] have also been used. Following Bingham [3], we note that F (Λ) is proportional to a hyper-geometric function of matrix argument, with series expansion…”

Section: A the Normalization Constantmentioning

confidence: 99%

Monte Carlo Pose Estimation with Quaternion Kernels and the Bingham Distribution

Glover¹,

Rusu²

2011

Robotics: Science and Systems VII

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Abstract-The success of personal service robotics hinges upon reliable manipulation of everyday household objects, such as dishes, bottles, containers, and furniture. In order to accurately manipulate such objects, robots need to know objects' full 6-DOF pose, which is made difficult by clutter and occlusions. Many household objects have regular structure that can be used to effectively guess object pose given an observation of just a small patch on the object. In this paper, we present a new method to model the spatial distribution of oriented local features on an object, which we use to infer object pose given small sets of observed local features. The orientation distribution for local features is given by a mixture of Binghams on the hypersphere of unit quaternions, while the local feature distribution for position given orientation is given by a locally-weighted (Quaternion kernel) likelihood. Experiments on 3D point cloud data of cluttered and uncluttered scenes generated from a structured light stereo image sensor validate our approach.

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“…an other statistical distribution agree much better. The underlying distribution is the Bingham distribution (Bingham, 1964;Onstott, 1980;Kent, 1982Kent, ,1987 which has in minimum five moments (parameters). Its parameters include directions of highest, lowest, and intermediate data concentration and measures of ellipticity that can for example describe the girdle shape reflecting folding.…”

Section: Options and Strategies Towards Quantitative Geologymentioning

confidence: 99%