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networkTomography (version 0.2)

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.

See Also

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