spatial_spde: SPDE spatial field (Matern via triangular mesh)

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

SPDE spatial field (Matern via triangular mesh)

Description

Specify a continuous Matern spatial field using the SPDE approach (Lindgren, Rue & Lindstrom 2011). Builds a triangular mesh from observation coordinates, computes FEM matrices, and passes them to tulpa's SPDE Laplace engine with CHOLMOD sparse solver.

Usage

spatial_spde(
  coords,
  data = NULL,
  mesh = NULL,
  boundary = NULL,
  max_edge = NULL,
  cutoff = 0,
  nu = 1,
  prior_range = NULL,
  prior_sigma = NULL
)

Arguments

coords	A formula ~ x + y or a two-column matrix of coordinates.
data	Optional data.frame for formula evaluation.
mesh	A pre-built tulpa_mesh object. If NULL (default), a mesh is built automatically from coords.
boundary	Optional boundary: a two-column matrix of polygon vertices, an sf polygon, or NULL for convex hull with extension.
max_edge	Maximum edge length for mesh refinement. A single value or c(inner, outer).
cutoff	Minimum distance between mesh vertices. Default 0.
nu	Matern smoothness parameter. A positive number. Integer nu (1, 2, 3, ...) gives an exact FEM construction (operator order alpha = nu + 1). Fractional nu (e.g. 0.5, 1.5) uses the operator-based rational SPDE approximation with BRASIL best-rational coefficients (Bolin & Kirchner 2020; Hofreither 2021); supported by the Laplace fitter fit_spde() (single-point and nested over range/sigma). NUTS and analytic marginal SEs remain integer-only. Default 1.
prior_range	PC prior on the spatial range, c(U, alpha) with P(range < U) = alpha. NULL (the default) anchors it on the data: U is a fifth of the diagonal of the coordinates' bounding box and alpha = 0.5, so U is the prior median.
prior_sigma	PC prior on the marginal standard deviation, c(U, alpha) with P(sigma > U) = alpha. NULL (the default) is c(3, 0.01), the engine's prior on every field scale.

Value

A tulpa_spatial object with type "spde".

Examples

set.seed(42)
coords <- cbind(runif(50), runif(50))
spec <- spatial_spde(coords)
print(spec)

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.