real.fft

Fast calculation of the real Fourier transform. This is a wrapper
 function for a C function which uses the complex FFT function from the 'fftw3' library.

Functionality for spatio-temporal modeling of large data sets is provided. A Gaussian process in space and time is defined through a stochastic partial differential equation (SPDE). The SPDE is solved in the spectral space, and after discretizing in time and space, a linear Gaussian state space model is obtained. When doing inference, the main computational difficulty consists in evaluating the likelihood and in sampling from the full conditional of the spectral coefficients, or equivalently, the latent space-time process. In comparison to the traditional approach of using a spatio-temporal covariance function, the spectral SPDE approach is computationally advantageous. See Sigrist, Kuensch, and Stahel (2015) <doi:10.1111/rssb.12061> for more information on the methodology. This package aims at providing tools for two different modeling approaches. First, the SPDE based spatio-temporal model can be used as a component in a customized hierarchical Bayesian model (HBM). The functions of the package then provide parameterizations of the process part of the model as well as computationally efficient algorithms needed for doing inference with the HBM. Alternatively, the adaptive MCMC algorithm implemented in the package can be used as an algorithm for doing inference without any additional modeling. The MCMC algorithm supports data that follow a Gaussian or a censored distribution with point mass at zero. Covariates can be included in the model through a regression term.

Fabio Sigrist

spate

Spatio-Temporal Modeling of Large Data Using a Spectral SPDE
Approach

real.fft function

<dl> <dt>w</dt>
<dd>A spatial field in a stacked vector of length N=n^2.</dd><dt>n</dt>
<dd>Number of grid points on each axis. n x n is the total number of spatial points.</dd> <dt>inv</dt>
<dd>Indicates whether the inverse Fourier transform should be calculated or not.</dd> <dt>indFFT</dt>
<dd>A list of containing vectors of natural numbers representing indices
used to transform between the real and the complex Fourier transform.</dd></dl>

Arguments

Author

Fast calculation of the two-dimensional real Fourier transform. — real.fft

<dl>

 <dt>w</dt>
<dd>A spatial field in a stacked vector of length N=n^2.</dd>

<dt>n</dt>
<dd>Number of grid points on each axis. n x n is the total number of spatial points.</dd>

 <dt>inv</dt>
<dd>Indicates whether the inverse Fourier transform should be calculated or not.</dd>

 <dt>indFFT</dt>
<dd>A list of containing vectors of natural numbers representing indices
used to transform between the real and the complex Fourier transform.</dd>

</dl>

real.fft: Fast calculation of the two-dimensional real Fourier transform.

Description

Usage

Value

Arguments

Author

Examples