*Martin Lysy, Bryan Yates*

Density evaluation and random number generation for the Matrix-Normal Inverse-Wishart (MNIW) distribution, as well as the the Matrix-Normal, Matrix-T, Wishart, and Inverse-Wishart distributions. Core calculations are implemented in a portable (header-only) C++ library, with matrix manipulations using the **Eigen** library for linear algebra. Also provided is a Gibbs sampler for Bayesian inference on a random-effects model with Matrix-Normal observations.

To install the CRAN version (1.0.1):

`install.packages("mniw", INSTALL_opts = "--install-tests")`

To install the latest development version: first install the **devtools**, then:

`devtools::install_github("mlysy/mniw", INSTALL_opts = "--install-tests")`

The primary advantage of the **mniw** package is that it “vectorizes” over its input arguments. Take for example the simulation of a Wishart distribution, which can be done with the built-in R function `stats::rWishart()`

:

```
n <- 10
p <- 3
nu <- 6
# produces an array of size p x p x n
Psi <- stats::rWishart(n = n, df = nu, Sigma = diag(p))
```

Now suppose we want to generate Wishart random variables each with a different `Sigma`

:

```
# Vectorizing over the 'Sigma' argument
X <- apply(Psi, 3, stats::rWishart, n = 1, df = nu)
X <- array(X, dim = c(p, p, n))
```

However, the code above is both slow for large `n`

, and inconvenient due to the reshaping of the `apply()`

output. The equivalent code using **mniw** is:

`X <- rwish(n, df = nu, Psi = Psi) # produces an array of size p x p x n`

It is both simpler, and much faster for large `n`

and `p`

.

The other functions in **mniw** behave much the same way. A complete description of the distributions provided by the package is available here.