smoothed_EM: Run EM algorithm to obtain MLE (single time) for smoothed...

Description Usage Arguments Value References See Also

View source: R/caoEtAl.R

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

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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.