fm_gmrf {fmesher}

SPDE, GMRF, and Matérn process methods

Description

Methods for SPDEs and GMRFs.

Usage

fm_matern_precision(x, alpha, rho, sigma)

fm_matern_sample(x, alpha = 2, rho, sigma, n = 1, loc = NULL)

fm_covariance(Q, A1 = NULL, A2 = NULL, partial = FALSE)

fm_sample(n, Q, mu = 0, constr = NULL)

Arguments

x

A mesh object, e.g. from fm_mesh_1d() or fm_mesh_2d().

alpha

The SPDE operator order. The resulting smoothness index is nu = alpha - dim / 2.

rho

The Matérn range parameter (scale parameter kappa = sqrt(8 * nu) / rho)

sigma

The nominal Matérn std.dev. parameter

n

The number of samples to generate

loc

locations to evaluate the random field, compatible with fm_evaluate(x, loc = loc, field = ...)

Q

A precision matrix

A1, A2

Matrices, typically obtained from fm_basis() and/or fm_block().

partial

If TRUE, compute the partial inverse of Q, i.e. the elements of the inverse corresponding to the non-zero pattern of Q. (Note: This can be done efficiently with the Takahashi recursion method, but to avoid an RcppEigen dependency this is currently disabled, and a slower method is used until the efficient method is reimplemented.)

mu

Optional mean vector

constr

Optional list of constraint information, with elements A and e. Should only be used for a small number of exact constraints.

Value

fm_matern_sample() returns a matrix, where each column is a sampled field. If loc is NULL, the fm_dof(mesh) basis weights are given. Otherwise, the evaluated field at the nrow(loc) locations loc are given (from version ⁠0.1.4.9001⁠)

Functions

• fm_matern_precision(): Construct the (sparse) precision matrix for the basis weights for Whittle-Matérn SPDE models. The boundary behaviour is determined by the provided mesh function space.

• fm_matern_sample(): Simulate a Matérn field given a mesh and covariance function parameters, and optionally evaluate at given locations.

• fm_covariance(): Compute the covariance between "A1 x" and "A2 x", when x is a basis vector with precision matrix Q.

• fm_sample(): Generate n samples based on a sparse precision matrix Q

Examples

library(Matrix)
mesh <- fm_mesh_1d(-20:120, degree = 2)
Q <- fm_matern_precision(mesh, alpha = 2, rho = 15, sigma = 1)
x <- seq(0, 100, length.out = 601)
A <- fm_basis(mesh, x)
plot(x,
  as.vector(Matrix::diag(fm_covariance(Q, A))),
  type = "l",
  ylab = "marginal variances"
)

plot(x,
  fm_evaluate(mesh, loc = x, field = fm_sample(1, Q)[, 1]),
  type = "l",
  ylab = "process sample"
)