rnorm_qinv_l_eigen: Sample from multivariate normal distribution given symmetric...

In dcbdan/s525: Implementation of common Bayesian models

Description

Sample from multivariate normal distribution with mean Q^{-1}l and covariance matrix Q^{-1} where Q = UDU^t

Usage

rnorm_qinv_l_eigen <- function(
  n,
  U,
  d,
  l)

Arguments

n	number of elements to generate
U	orthogonal matrix such that Q = UDU^t
d	p by 1 vector, D = diag(d) and Q = UDU^t
l	p by 1 vector

Details

This function is useful to sample from N((Q + sI)^{-1}l, (Q + sI)^{-1}) given the eigen decomposition of Q

Value

x	An p x 1 vector if n=1 otherwise a n by p matrix

Examples

  W = cbind(c(10,1), c(1,10))
  ee = eigen(W, symmetric = TRUE)
  U = ee$vectors
  d = ee$values
  crossprod(U)

  solve(W)
  U 

  l = c(50,100)
  m = U 
  ret = rnorm_qinv_l_eigen(50000, U, d, l)
  mean(ret[,1] - m[1])
  mean(ret[,2] - m[2])
  sum(cov(ret) - (U 

dcbdan/s525 documentation built on May 19, 2019, 10:48 p.m.