Description Usage Arguments Details Value References See Also Examples

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

1 2 | ```
dyangberger(x, log=FALSE)
dyangbergerc(x, log=FALSE)
``` |

`x` |
This is the |

`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`

1 2 3 | ```
library(LaplacesDemon)
X <- matrix(c(1,0.8,0.8,1), 2, 2)
dyangberger(X, log=TRUE)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.