Yang-Berger Distribution
This is the density function for the Yang-Berger prior distribution for a covariance matrix or precision matrix.
dyangberger(x, log=FALSE) dyangbergerc(x, log=FALSE)
x |
This is the k x k positive-definite
covariance matrix or precision matrix for |
log |
Logical. If |
Application: Continuous Multivariate
Density: p(theta) = 1 / |theta|^(prod (d[j] - d[j-1])), where d are increasing eigenvalues. See equation 13 in Yang and Berger (1994).
Inventor: Yang and Berger (1994)
Notation 1: p(theta) ~ YB
Mean:
Variance:
Mode:
Yang and Berger (1994) derived a least informative prior (LIP) for a covariance matrix or precision matrix. The Yang-Berger (YB) distribution does not have any parameters. It is a reference prior for objective Bayesian inference. The Cholesky parameterization is also provided here.
The YB prior distribution results in a proper posterior. It involves an eigendecomposition of the covariance matrix or precision matrix. It is difficult to interpret a model that uses the YB prior, due to a lack of intuition regarding the relationship between eigenvalues and correlations.
Compared to Jeffreys prior for a covariance matrix, this reference prior encourages equal eigenvalues, and therefore results in a covariance matrix or precision matrix with a better shrinkage of its eigenstructure.
dyangberger and dyangbergerc give the density.
Yang, R. and Berger, J.O. (1994). "Estimation of a Covariance Matrix using the Reference Prior". Annals of Statistics, 2, p. 1195-1211.
dinvwishart and
dwishart
library(LaplacesDemon) X <- matrix(c(1,0.8,0.8,1), 2, 2) dyangberger(X, log=TRUE)
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