ffbs: Forward Filtering Backward Sampling algorithm.
In spate: Spatio-Temporal Modeling of Large Data Using a Spectral SPDE Approach

ffbs	R Documentation

Forward Filtering Backward Sampling algorithm.

Description

Forward Filtering Backward Sampling algorithm for sampling from the joint full conditional of the hidden state of a linear, Gaussian state space model. To be more specific, one samples from P[\alpha|.] where \alpha is specified through

y_t = lp_t + H xi_t + nu_t, \nu_t ~ N(0,\Omega)

and

\alpha_t = G \alpha_{t-1} + \epsilon_t, \epsilon_t ~ N(0,\Sigma).

Usage

ffbs(y, lp, G, Sigma, H, Omega, N = dim(y)[2],T = dim(y)[1],
      NF = dim(G)[1], lglk = FALSE, BwSp = TRUE, filt = FALSE)

Arguments

`y`	Observed data in an T x N matrix with columns and rows corresponding to time and space, respectively.
`lp`	Mean (linear predictor) in an T x N matrix with columns and rows corresponding to time and space, respectively.
`G`	Propagator matrix of the latent process `\alpha`.
`Sigma`	Innovation covariance matrix of the latent process `\alpha`.
`H`	Observation matrix relating y to `\alpha`.
`Omega`	Covariance matrix of the observation error `\nu`.
`N`	Number of points in space.
`T`	Number of points in time.
`NF`	Dimension of the latent process `\alpha`.
`lglk`	Logical; if 'TRUE' the value of the log-likelihood is returned as well.
`BwSp`	Logical; if 'TRUE' a sample from the full conditional of `\alpha` is returned.
`filt`	Logical; if 'TRUE' the filtered values for `\alpha` are returned.

Details

In the context of the SPDE, \alpha are the Fourier coefficients.

Value

A list with entries (depending on whether 'lglk', 'BwSp', 'filt' are 'TRUE' or 'FALSE'):

`simAlpha`	A T x N matrix with a sample from the full conditional of latent process `\alpha`,
`ll`	The evaluated log-likelihood,
`mtt`	A T x N matrix with the mean of the full conditional of latent process `\alpha`.