Matern SPDE model object for INLA

Description

Create an inla.spde2 model object for a Matern model. Use inla.spde2.pcmatern instead for a PC prior for the parameters.

Usage

inla.spde2.matern(
  mesh,
  alpha = 2,
  param = NULL,
  constr = FALSE,
  extraconstr.int = NULL,
  extraconstr = NULL,
  fractional.method = c("parsimonious", "null"),
  B.tau = matrix(c(0, 1, 0), 1, 3),
  B.kappa = matrix(c(0, 0, 1), 1, 3),
  prior.variance.nominal = 1,
  prior.range.nominal = NULL,
  prior.tau = NULL,
  prior.kappa = NULL,
  theta.prior.mean = NULL,
  theta.prior.prec = 0.1,
  n.iid.group = 1,
  ...
)

inla.spde2.theta2phi0(spde, theta)

inla.spde2.theta2phi1(spde, theta)

inla.spde2.theta2phi2(spde, theta)

Arguments

Details

This method constructs a Matern SPDE model, with spatial scale parameter \kappa(u) and variance rescaling parameter \tau(u).

(\kappa^2(u)-\Delta)^{\alpha/2}(\tau(u)

x(u))=W(u)

Stationary models are supported for 0 < \alpha \leq 2, with spectral approximation methods used for non-integer \alpha, with approximation method determined by fractional.method.

Non-stationary models are supported for \alpha=2 only, with

• \log\tau(u) = B^\tau_0(u) + \sum_{k=1}^p B^\tau_k(u) \theta_k

• \log\kappa(u) = B^{\kappa}_0(u) + \sum_{k=1}^p B^{\kappa}_k(u) \theta_k

The same parameterisation is used in the stationary cases, but with B^\tau_0, B^\tau_k, B^\kappa_0, and B^\tau_k constant across u.

Integration and other general linear constraints are supported via the constr, extraconstr.int, and extraconstr parameters, which also interact with n.iid.group.

Value

An inla.spde2 object.

Functions

• inla.spde2.theta2phi0(): Convert from theta vector to phi0 values in the internal spde2 model representation

• inla.spde2.theta2phi1(): Convert from theta vector to phi1 values in the internal spde2 model representation

• inla.spde2.theta2phi2(): Convert from theta vector to phi2 values in the internal spde2 model representation

Author(s)

Finn Lindgren finn.lindgren@gmail.com

See Also

fmesher::fm_mesh_2d_inla(), fmesher::fm_rcdt_2d_inla(), fmesher::fm_mesh_1d(), fmesher::fm_basis(), inla.spde2.pcmatern(), inla.spde2.generic()

Examples

n <- 100
field.fcn <- function(loc) (10 * cos(2 * pi * 2 * (loc[, 1] + loc[, 2])))
loc <- matrix(runif(n * 2), n, 2)
## One field, 2 observations per location
idx.y <- rep(1:n, 2)
y <- field.fcn(loc[idx.y, ]) + rnorm(length(idx.y))

mesh <- fm_rcdt_2d_inla(loc, refine = list(max.edge = 0.05))
spde <- inla.spde2.matern(mesh)
data <- list(y = y, field = mesh$idx$loc[idx.y])
formula <- y ~ -1 + f(field, model = spde)
result <- inla(formula, data = data, family = "normal")

## Plot the mesh structure:
plot(mesh)

if (require(rgl)) {
    col.pal <- colorRampPalette(c("blue", "cyan", "green", "yellow", "red"))
    ## Plot the posterior mean:
    plot(mesh,
        rgl = TRUE,
        result$summary.random$field[, "mean"],
        color.palette = col.pal
    )
    ## Plot residual field:
    plot(mesh,
        rgl = TRUE,
        result$summary.random$field[, "mean"] - field.fcn(mesh$loc),
        color.palette = col.pal
    )
}

result.field <- inla.spde.result(result, "field", spde)
plot(result.field$marginals.range.nominal[[1]])