Description Usage Arguments Value References See Also
Computes gradient of Q-function with respect to log(c(lambda,phi)) for EM algorithm from Cao et al. (2000) for their smoothed model.
1 | grad_smoothed(logtheta, c, M, rdiag, eta0, sigma0, V, eps.lambda, eps.phi)
|
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 |
numeric vector of same length as logtheta containing calculated gradient
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.
Other CaoEtAl: Q_iid
;
Q_smoothed
; R_estep
;
grad_iid
; locally_iid_EM
;
m_estep
; phi_init
;
smoothed_EM
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