locally_iid_EM: Run EM algorithm to obtain MLE for locally IID model of Cao...
In networkTomography: Tools for network tomography

Description Usage Arguments Value References See Also

Runs EM algorithm to compute MLE for the locally IID model of Cao et al. (2000). Uses numerical optimization of Q-function for each M-step with analytic computation of its gradient.

1 2	locally_iid_EM(Y, A, lambda0, phi0 = NULL, c = 2, maxiter = 1000, tol = 1e-06, epsilon = 0.01, method = "L-BFGS-B", checkActive = FALSE)

`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
`lambda0`	initial vector of values (length k) for lambda; `ipfp` is a good way to obtain this
`phi0`	initial value for covariance scale phi; initializes automatically using `phi_init` if NULL, but you can likely do better
`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
`epsilon`	numeric nugget to add to diagonal of covariance for numerical stability
`method`	optimization method to use (in optim calls)
`checkActive`	logical check for deterministically known OD flows

list with 3 elements: lambda, the estimated value of lambda; phi, the estimated value of phi; and iter, the number of iterations run

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; m_estep; phi_init; smoothed_EM