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 |

`log` |
Logical. If |

### Details

Application: Continuous Multivariate

Density:

`p(\theta) = \frac{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:

`\theta \sim \mathcal{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)
```

*LaplacesDemon*version 16.1.6 Index]