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

In awblocker/networkTomography: Tools for Network Tomography

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()

awblocker/networkTomography documentation built on May 14, 2022, 10:05 p.m.