Q_smoothed: Q function for smoothed EM algorithm of Cao et al. (2000)

In networkTomography: Tools for network tomography

Description

Computes the Q function (expected log-likelihood) for the EM algorithm of Cao et al. (2000) for their smoothed model.

Usage

Q_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 value of Q function; not vectorized in any way

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; R_estep; grad_iid; grad_smoothed; locally_iid_EM; m_estep; phi_init; smoothed_EM

networkTomography documentation built on May 2, 2019, 3:28 a.m.