See details for model. Notation: N is number of samples,
D is the dimension of the response, Q is number
of covariates.
Arguments
- Y
matrix of dimension D x N
- X
matrix of covariates of dimension Q x N
- Theta
matrix of prior mean of dimension D x Q
- Gamma
covariance matrix of dimension Q x Q
- Xi
covariance matrix of dimension D x D
- upsilon
scalar (must be > D-1) degrees of freedom for InvWishart prior
- n_samples
number of samples to draw (default: 2000)
Value
List with components
Lambda Array of dimension (D-1) x Q x n_samples (posterior samples)
Sigma Array of dimension (D-1) x (D-1) x n_samples (posterior samples)
Details
$$Y \sim MN_{D-1 \times N}(Lambda*X, Sigma, I_N)$$
$$Lambda \sim MN_{D-1 \times Q}(Theta, Sigma, Gamma)$$
$$Sigma \sim InvWish(upsilon, Xi)$$
This function provides a means of sampling from the posterior distribution of
Lambda and Sigma.
Examples
sim <- pibble_sim()
eta.hat <- t(alr(t(sim$Y+0.65)))
fit <- conjugateLinearModel(eta.hat, sim$X, sim$Theta, sim$Gamma,
sim$Xi, sim$upsilon, n_samples=2000)