lgf1: First order LGF

In dajmcdon/spasm: Implements the Laplace-Gaussian filter for sparse, additive, state-space models

Description

Given a sparse-spline representation of the observation equation, this function performs filtering to derive the conditional distributions of the filtered (x_{t|t}) and predicted (x_{t|t-1}) hidden states.

Usage

lgf1(Y, out.spam, Tt, HHinv, GGt, x0, P0)

Arguments

Y	the observed data, a Nxd matrix
out.spam	the sparse additive spline model associated with the observation equation, as produced by spam
Tt	the state transition matrix, pxp
HHinv	the inverse of the observation noise variance matrix
GGt	the transition noise variance matris
x0	prior mean of the state variables
P0	prior variance of the state variables

Value

A list with components xt and xtt, the predicted and filtered state means respectively and Pt and Ptt, the associated variances.

Examples

someData = generateSPASM(100,3,4)
SPAMfit = spam(someData$y, someData$x)
filt = lgf1(someData$y, SPAMfit, someData$Tt,
  solve(someData$HHt), someData$GGt, rep(0,3), diag(1,3))
matplot(someData$x, ty='l', col=1, lty=1)
matlines(filt$xtt, col=2, lty=3)

dajmcdon/spasm documentation built on May 6, 2019, 1:31 a.m.