Laplace approximation for Bessel functions of matrix argument
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In this article, the authors derived Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel Av, matrix bessel Bv, and the type II confluent hypergeometric function, Ψ.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2003-06-15 and is currently open access. It has received 44 citations till now. The article focuses on the topics: Hypergeometric function of a matrix argument & Laplace expansion.read more
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Modeling Realized Covariances and Returns
Xin Jin,John M. Maheu +1 more
TL;DR: In this article, the authors proposed new dynamic component models of returns and realized covariance (RCOV) matrices based on time-varying Wishart distributions, which provide superior density forecasts for returns from forecast horizons of 1 day to 3 months ahead as well as improved point forecasts for realized covariances.
Proceedings Article
Infinite Positive Semidefinite Tensor Factorization for Source Separation of Mixture Signals
TL;DR: A nonparametric Bayesian model based on a gamma process that can instantiate only a limited number of necessary bases from the infinitely many bases assumed to exist is proposed and a variational Bayesian algorithm for closed-form posterior inference and a multiplicative update rule for maximum-likelihood estimation is derived.
Journal ArticleDOI
On Bayesian principal component analysis
Vaclav Smidl,Anthony Quinn +1 more
TL;DR: The posterior distribution of the PCs is found to be of the von-Mises-Fisher type, leading to a stable and efficient orthogonal variational PCA (OVPCA) algorithm that provides the required inferences.
Journal ArticleDOI
Saddlepoint approximations for the normalizing constant of Fisher-Bingham distributions on products of spheres and Stiefel manifolds
TL;DR: In the challenging high-dimensional settings considered in this paper the saddlepoint approximations perform very well in all examples considered and are equivalent to a multivariate saddlepoint density approximation for the joint distribution of a set of quadratic forms in normal variables.
Journal ArticleDOI
BPSK Bit Error Outage over Nakagami-m Fading Channels in Lognormal Shadowing Environments
TL;DR: A simple yet tight approximation of the bit error probability (BEP) for binary phase shift keying (BPSK) over a frequency-flat Nakagami-m fading channel is derived, which facilitates the derivation of a tight lower bound of the BEO in presence of lognormal shadowing in closed form.
References
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Handbook of Mathematical Functions
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Aspects of multivariate statistical theory
TL;DR: In this paper, the authors present a set of standard tests on Covariance Matrices and Mean Vectors, and test independence between k Sets of Variables and Canonical Correlation Analysis.
Journal ArticleDOI
Accurate Approximations for Posterior Moments and Marginal Densities
Luke Tierney,Joseph B. Kadane +1 more
TL;DR: These approximations to the posterior means and variances of positive functions of a real or vector-valued parameter, and to the marginal posterior densities of arbitrary parameters can also be used to compute approximate predictive densities.