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networkTomography (version 0.3)

llCalibration: Evaluate marginal log-likelihood for calibration SSM

Description

Evaluates marginal log-likelihood for calibration SSM of Blocker & Airoldi (2011) using Kalman filtering. This is very fast and numerically stable, using the univariate Kalman filtering and smoothing functions of KFAS with Fortran implementations.

Usage

llCalibration(theta, Ft, yt, Zt, Rt, k = ncol(Ft), tau = 2, initScale = 1/(1 - diag(Ft)^2), nugget = sqrt(.Machine$double.eps))

Arguments

theta
numeric vector (length k+1) of parameters. theta[-1] = log(lambda), and theta[1] = log(phi)
Ft
evolution matrix (k x k) for OD flows; include fixed
yt
matrix (k x n) of observed link loads, one observation per column
Zt
observation matrix for system; should be routing matrix A
Rt
covariance matrix for observation equation; typically small and fixed
k
integer number of OD flows to infer
tau
numeric power parameter for mean-variance relationship
initScale
numeric inflation factor for time-zero state covariance; defaults to steady-state variance setting
nugget
small positive value to add to diagonal of state evolution covariance matrix to ensure numerical stability

Value

numeric marginal log-likelihood obtained via Kalman smoothing

References

A.W. Blocker and E.M. Airoldi. Deconvolution of mixing time series on a graph. Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11) 51-60, 2011.

See Also

Other calibrationModel: calibration_ssm; mle_filter