grad_iid: Compute analytic gradient of Q-function for locally IID EM...

In awblocker/networkTomography: Tools for Network Tomography

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.

See Also

Other CaoEtAl: Q_iid(), Q_smoothed(), R_estep(), grad_smoothed(), locally_iid_EM(), m_estep(), phi_init(), smoothed_EM()

awblocker/networkTomography documentation built on May 14, 2022, 10:05 p.m.