llCalibration: Evaluate marginal log-likelihood for calibration SSM

Description Usage Arguments Value References See Also

View source: R/ssmMle.R

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

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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


networkTomography documentation built on May 2, 2019, 3:28 a.m.