grad_iid: Compute analytic gradient of Q-function for locally IID EM algorithm of Cao
et al. (2000)
Description
Computes gradient of Q-function with respect to
log(c(lambda,phi)) for EM algorithm from Cao et al. (2000)
for their locally IID model.
Usage
grad_iid(logtheta, c, M, rdiag, epsilon)
Arguments
logtheta
numeric vector (length k+1) of
log(lambda) (1:k) and log(phi) (last entry)
c
power parameter in model of Cao et al. (2000)
M
matrix (n x k) of conditional expectations for
OD flows, one time per row
rdiag
numeric vector (length k) containing
diagonal of conditional covariance matrix R
epsilon
numeric nugget to add to diagonal of
covariance for numerical stability
Value
numeric vector of same length as logtheta containing
calculated gradient
References
J. Cao, D. Davis, S. Van Der Viel, and B. Yu. Time-varying
network tomography: router link data. Journal of the
American Statistical Association, 95:1063-75, 2000.