R: Yang-Berger Distribution

dist.YangBerger {LaplacesDemon} | R Documentation

## Yang-Berger Distribution

### Description

This is the density function for the Yang-Berger prior distribution for a covariance matrix or precision matrix.

### Usage

    dyangberger(x, log=FALSE)
    dyangbergerc(x, log=FALSE)

### Arguments

`x` | This is the k x k positive-definite covariance matrix or precision matrix for `dyangberger` or the Cholesky factor U of the covariance matrix or precision matrix for `dyangbergerc`.
`log` | Logical. If `log=TRUE`, then the logarithm of the density is returned.

### Details

- 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.

### Value

`dyangberger` and `dyangbergerc` give the density.

### References

Yang, R. and Berger, J.O. (1994). "Estimation of a Covariance Matrix using the Reference Prior". Annals of Statistics, 2, p. 1195-1211.

### See Also

`dinvwishart` and `dwishart`

### Examples

    library(LaplacesDemon)
    X <- matrix(c(1,0.8,0.8,1), 2, 2)
    dyangberger(X, log=TRUE)

[Package LaplacesDemon version 16.1.1 Index]