spacetime: Ngme space-time non-separable model specification
In ngme2: Linear Latent Non-Gaussian Models with Flexible Distributions

spacetime

R Documentation

Ngme space-time non-separable model specification

Description

Implements a non-separable space-time model based on the advection-diffusion SPDE with first-order derivative in time. The model combines temporal and spatial components through a finite difference method (implicit Euler) for temporal discretization and finite element method (continuous Galerkin) for spatial discretization. When advection dominates diffusion, the "Streamline Diffusion" stabilization technique is applied.

Usage

spacetime(
  mesh,
  lambda = 1,
  alpha = 2,
  cc = 1,
  kappa = 1,
  fix_gamma = FALSE,
  theta_gamma_x = 0,
  theta_gamma_y = 0,
  shared_theta_gamma = FALSE,
  B_gamma_x = matrix(1, nrow = mesh[[2]]$n, ncol = 1),
  B_gamma_y = matrix(1, nrow = mesh[[2]]$n, ncol = 1),
  B_gamma_x_list = NULL,
  B_gamma_y_list = NULL,
  stabilization = TRUE
)

Arguments

`mesh`	A list of two objects: mesh_t - The temporal mesh mesh_s - The spatial mesh
`lambda`	The spatial damping parameter.
`alpha`	2 or 4, SPDE smoothness parameter.
`cc`	Parameter c in the SPDE.
`kappa`	Kappa parameter from Matern SPDE.
`fix_gamma`	TRUE if fix gamma (advection term), FALSE if estimate gamma.
`theta_gamma_x`	The x component of the advection term: `gamma_x = B_gamma_x %*% theta_gamma_x`.
`theta_gamma_y`	The y component of the advection term: `gamma_y = B_gamma_y %*% theta_gamma_y`.
`shared_theta_gamma`	TRUE if share the same theta_gamma for all time nodes. (theta_gamma_x and theta_gamma_y will be the same)
`B_gamma_x`	The design matrix for the x component of the advection term.
`B_gamma_y`	The design matrix for the y component of the advection term.
`B_gamma_x_list`	A list of design matrices for the x component of the advection term on every time node, length(B_gamma_x_list) == nt-1.
`B_gamma_y_list`	A list of design matrices for the y component of the advection term on every time node, length(B_gamma_y_list) == nt-1.
`stabilization`	TRUE if using a stabilization term (for implicit Euler).

Details

The model is particularly useful for large space-time datasets in environmental science, offering computationally efficient methods for parameter estimation, kriging prediction, and conditional simulations.

For details, see \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.spasta.2024.100847")}