llCalibration: Evaluate marginal log-likelihood for calibration SSM

In awblocker/networkTomography: Tools for Network Tomography

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()

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