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

## 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

 ```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") ```

## 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`

networkTomography documentation built on May 29, 2017, 4:56 p.m.