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networkTomography (version 0.3)

grad_smoothed: Compute analytic gradient of Q-function for smoothed 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 smoothed model.

Usage

grad_smoothed(logtheta, c, M, rdiag, eta0, sigma0, V, eps.lambda, eps.phi)

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
eta0
numeric vector (length k+1) containing value for log(c(lambda, phi)) from previous time (or initial value)
sigma0
covariance matrix (k+1 x k+1) of log(c(lambda, phi)) from previous time (or initial value)
V
evolution covariance matrix (k+1 x k+1) for log(c(lambda, phi)) (random walk)
eps.lambda
numeric small positive value to add to lambda for numerical stability; typically 0
eps.phi
numeric small positive value to add to phi for numerical stability; typically 0

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_iid; locally_iid_EM; m_estep; phi_init; smoothed_EM