Learn R Programming

networkTomography (version 0.3)

smoothed_EM: Run EM algorithm to obtain MLE (single time) for smoothed model of Cao et al. (2000)

Description

Runs EM algorithm to compute MLE for the smoothed model of Cao et al. (2000). Uses numerical optimization of Q-function for each M-step with analytic computation of its gradient. This performs estimation for a single time point using output from the previous one.

Usage

smoothed_EM(Y, A, eta0, sigma0, V, c = 2, maxiter = 1000, tol = 1e-06, eps.lambda = 0, eps.phi = 0, method = "L-BFGS-B")

Arguments

Y
matrix (h x k) of observations in local window; columns correspond to OD flows, and rows are individual observations
A
routing matrix (m x k) for network being analyzed
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)
c
power parameter in model of Cao et al. (2000)
maxiter
maximum number of EM iterations to run
tol
tolerance (in relative change in Q function value) for stopping EM iterations
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
method
optimization method to use (in optim calls)

Value

list with 5 elements: lambda, the estimated value of lambda; phi, the estimated value of phi; iter, the number of iterations run; etat, log(c(lambda, phi)); and sigmat, the inverse of the Q functions Hessian at its mode

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; grad_smoothed; locally_iid_EM; m_estep; phi_init