Description Usage Arguments Value Author(s)

Forward Filtering Backward Sampling algorithm for sampling from the
joint full conditional of the coefficients *α* and for
evaluation of the log-likelihood.

1 2 |

`w` |
Observed data or latent process w (depending on which data model is used) in an T x n*n matrix with columns and rows (points on a grid stacked into a vector) corresponding to time and space, respectively. |

`wFT` |
Vector of length T*n*n containing the real Fourier transform of 'w'. |

`spec` |
Spectrum of the innovations |

`Gvec` |
The propagator matrix G in vector format obtained from 'get.G.vec'. If 'Gvec' is not given, it is constructed based on 'par'. |

`tau2` |
Measurement error variance tau2. If 'NULL'; tau2=par[9]. |

`par` |
Vector of parameters for the SPDE in the following order: rho_0, sigma^2, zeta, rho_1, gamma, alpha, mu_x, mu_y, tau^2. If 'spec' and 'Gvec' are given, 'par' will not be used. |

`n` |
Number of grid points on each axis. n*n is the total number of spatial points. |

`T` |
Number of points in time. |

`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 |

`NF` |
Number of Fourier functions used. |

`indCos` |
Vector of integers indicating the position cosine terms in the 1:NF real Fourier functions. The first 'ns' cosine wavenumbers in 'wave' are not included in 'indCos'. |

`ns` |
Number of real Fourier functions that have only a cosine and no sine term. 'ns' is maximal 4. |

`nu` |
Smoothness parameter of the Matern covariance function for the innovations. By default this equals 1 corresponding to the Whittle covariance function. |

`dt` |
Temporal lag between two time points. By default, this equals 1. |

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

`simAlpha` |
A T x n*n matrix with a sample from the full conditional
of latent process |

`ll` |
The evaluated log-likelihood, |

Fabio Sigrist

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