# Wishart: The Wishart Distribution In nimble: MCMC, Particle Filtering, and Programmable Hierarchical Modeling

 Wishart R Documentation

## The Wishart Distribution

### Description

Density and random generation for the Wishart distribution, using the Cholesky factor of either the scale matrix or the rate matrix.

### Usage

```dwish_chol(x, cholesky, df, scale_param = TRUE, log = FALSE)

rwish_chol(n = 1, cholesky, df, scale_param = TRUE)
```

### Arguments

 `x` vector of values. `cholesky` upper-triangular Cholesky factor of either the scale matrix (when `scale_param` is TRUE) or rate matrix (otherwise). `df` degrees of freedom. `scale_param` logical; if TRUE the Cholesky factor is that of the scale matrix; otherwise, of the rate matrix. `log` logical; if TRUE, probability density is returned on the log scale. `n` number of observations (only `n=1` is handled currently).

### Details

See Gelman et al., Appendix A or the BUGS manual for mathematical details. The rate matrix as used here is defined as the inverse of the scale matrix, S^{-1}, given in Gelman et al.

### Value

`dwish_chol` gives the density and `rwish_chol` generates random deviates.

### Author(s)

Christopher Paciorek

### References

Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2004) Bayesian Data Analysis, 2nd ed. Chapman and Hall/CRC.

Distributions for other standard distributions

### Examples

```df <- 40
ch <- chol(matrix(c(1, .7, .7, 1), 2))
x <- rwish_chol(1, ch, df = df)
dwish_chol(x, ch, df = df)

```

nimble documentation built on March 18, 2022, 8:03 p.m.