Sample a Gaussian vector using Bhattacharya et al. (2016)

Sample from N(mu, Sigma) where Sigma = solve(crossprod(Phi) + solve(D)) and mu = Sigma*crossprod(Phi, alpha):

Usage

sampleFastGaussian(Phi, Ddiag, alpha)

Arguments

Phi

n x p matrix (of predictors)

Ddiag

p x 1 vector of diagonal components (of prior variance)

alpha

n x 1 vector (of data, scaled by variance)

Value

Draw from N(mu, Sigma), which is p x 1, and is computed in O(n^2*p)

Note

Assumes D is diagonal, but extensions are available

References

Bhattacharya, Chakraborty, and Mallick (2016, <https://doi.org/10.1093/biomet/asw042>)