Conditional sampling for Multivariate-Normal Random-Effects model.

Sample from the conditional parameter distribution given the data and hyperparameters of the Multivariate-Normal Random-Effects (mNormRE) model (see Details).

rRxNorm(n, x, V, lambda, Sigma)

Arguments

n: Integer number of random samples to generate.
x: Data observations. Either a vector of length q or a n x q matrix. In the latter case each row is a different vector.
V: Observation variances. Either a matrix of size q x q or a q x q x n array.
lambda: Prior means. Either a vector of length q or an n x q matrix. In the latter case each row is a different mean. Defaults to zeros.
Sigma: Prior variances. Either a matrix of size q x q or a q x q x n array. Defaults to identity matrix.

Details

Consider the hierarchical multivariate normal model $$ \begin{array}{rcl} \boldsymbol{\mu} & \sim & \mathcal{N}(\boldsymbol{\lambda}, \boldsymbol{\Sigma}) \\ \boldsymbol{x} \mid \boldsymbol{\mu} & \sim & \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{V}). \end{array} $$ The Multivariate-Normal Random-Effects model $\boldsymbol{\mu} \sim \textrm{RxNorm}(\boldsymbol{x}, \boldsymbol{V}, \boldsymbol{\lambda}, \boldsymbol{\Sigma})$ on the random vector $\boldsymbol{\mu}_q$ is defined as the posterior distribution $p(\boldsymbol{\mu} \mid \boldsymbol{x}, \boldsymbol{\lambda}, \boldsymbol{\Sigma})$. This distribution is multivariate normal; for the mathematical specification of its parameters please see vignette("mniw-distributions", package = "mniw").

Examples

# data specification
q <- 5
y <- rnorm(q)
V <- rwish(1, diag(q), q+1)
# prior specification
lambda <- rep(0,q)
A <- diag(q)
n <- 10
# random sampling
rRxNorm(n, y, V, lambda, A)
#>             [,1]        [,2]       [,3]       [,4]       [,5]
#>  [1,] -0.3210119  0.25012776 -1.0832082  0.1766702  1.0026878
#>  [2,] -0.8477048 -0.06033919  0.7138509 -0.2359336  1.1328197
#>  [3,] -0.4833820 -0.37569205 -0.4355352  1.7421929  0.4572355
#>  [4,] -1.8244862 -0.36354547 -0.4464338  0.2354824  1.4738239
#>  [5,] -0.5469371  0.59287225 -0.4616895  1.9233230  1.5036275
#>  [6,] -0.6298590  0.74612003  0.1798659  0.3189405  1.3068775
#>  [7,] -1.3084676 -0.22138653 -0.7239478  1.7016159 -0.1686089
#>  [8,]  0.3120142  0.07852389 -1.2650215  2.1253076  0.9593281
#>  [9,]  0.3511071  0.02076032 -0.1073949  0.5507978  0.9456339
#> [10,] -1.6875222  1.21051823 -1.1897823  1.5921019  0.6289171