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

In awblocker/networkTomography: Tools for Network Tomography

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

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()

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