smoothed_EM: Run EM algorithm to obtain MLE (single time) for smoothed...
In networkTomography: Tools for network tomography

Description Usage Arguments Value References See Also

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.

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

`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)

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

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; grad_smoothed; locally_iid_EM; m_estep; phi_init