These are the density and random generation functions for the Huang-Wand prior distribution for a covariance matrix.
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This is a k x k positive-definite
covariance matrix Sigma for
This is a scalar degrees of freedom parameter
nu. The default is
This is a positive-only vector of scale parameters a of length k.
This is a positive-only vector of of scale hyperparameters
A of length k. Larger values result in a more
uninformative prior. A default, uninformative prior is
Application: Continuous Multivariate
Density: p(theta) = W^(-1)[nu+k-1](2*nu*diag(1/a)) G^(-1)(1/2, 1/A^2)
Inventor: Huang and Wand (2013)
Notation 1: theta ~ HW[nu](a, A)
Notation 2: p(theta) ~ HW[nu](theta | a, A)
Parameter 1: degrees of freedom nu
Parameter 2: scale a > 0
Parameter 3: scale A > 0
Huang and Wand (2013) proposed a prior distribution for a covariance matrix that uses a hierarchical inverse Wishart. This is a more flexible alternative to the inverse Wishart distribution, and the Huang-Wand prior retains conjugacy. The Cholesky parameterization is also provided here.
The Huang-Wand prior distribution alleviates two main limitations of an inverse Wishart distribution. First, the uncertainty in the diagonal variances of a covariance matrix that is inverse Wishart distributed is represented with only one degrees of freedom parameter, which may be too restrictive. The Huang-Wand prior overcomes this limitation. Second, the inverse Wishart distribution imposes a dependency between variance and correlation. The Huang-Wand prior lessens, but does not fully remove, this dependency.
The standard deviations of a Huang-Wand distributed covariance matrix are half-t distributed, as HT(nu, A). This is in accord with modern assumptions about distributions of scale parameters, and is also useful for sparse covariance matrices.
rhuangwand function allows either
A to be
a is missing, the covariance matrix is generated
from the hyperparameters. When
A is missing, the covariance
matrix is generated from the parameters.
dhuangwandc give the density, and
rhuangwandc generate random deviates.
Huang, A., Wand, M., et al. (2013), "Simple Marginally Noninformative Prior Distributions for Covariance Matrices". Bayesian Analysis, 8, p. 439–452.
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