| dNIW | R Documentation |
Get the density of a NIW sample. For a random vector mu, and a random matrix Sigma, the density function is defined as:
sqrt(2 pi^p |Sigma/k|)^{-1} exp(-1/2 (mu-m )^T (Sigma/k)^{-1} (mu-m)) (2^{(v p)/2} Gamma_p(v/2) |S|^{-v/2})^{-1} |Sigma|^{(-v-p-1)/2} exp(-1/2 tr(Sigma^{-1} S))
Where p is the dimension of mu and Sigma.
dNIW(mu, Sigma, m, k, v, S, LOG = TRUE)
mu |
numeric, the Gaussian sample. |
Sigma |
matrix, a symmetric positive definite matrix, the Inverse-Wishart sample. |
m |
numeric, mean of mu. |
k |
numeric, precision of mu. |
v |
numeric, degree of freedom of Sigma. |
S |
numeric, a symmetric positive definite scale matrix of Sigma, S is proportional to E(Sigma). |
LOG |
logical, return log density of LOG=TRUE, default TRUE. |
A numeric vector, the probability density of (mu,Sigma).
O'Hagan, Anthony, and Jonathan J. Forster. Kendall's advanced theory of statistics, volume 2B: Bayesian inference. Vol. 2. Arnold, 2004.
MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.
rNIW
S <- crossprod(matrix(rnorm(15),5,3)) Sigma <- crossprod(matrix(rnorm(15),5,3)) mu <- runif(3) m <- runif(3) dNIW(mu=mu,Sigma=Sigma,m=m,k=2,v=4,S=S,LOG = TRUE)