Recompute the weighted-L2 coefficients for an estimated kappa

Two-stage use of the weighted-L2 rational coefficients. The coefficients must not depend on kappa during estimation, since that would make the likelihood non-smooth in kappa, so they are computed at set-up for a conservative reference kappa. Once kappa has been estimated, this function recomputes them once for a reference derived from the estimate, for the final likelihood evaluation and for prediction.

Usage

update_rational_coefficients(object, kappa_ref = NULL, safety = 3, ...)

Arguments

object

A model created by matern.operators() with type_rational_approximation = "wl2".

kappa_ref

The new reference value. If NULL, the kappa of the object divided by safety is used.

safety

The safety factor applied to the kappa of the object when kappa_ref is not given.

...

Further arguments passed to update().

Value

The updated model.

Details

The reference must remain a lower bound for kappa, which is why the default divides the estimate by safety. A reference above the true kappa leaves part of the spectrum outside the fitted interval and the error grows by one to two orders of magnitude, whereas a reference below it degrades gracefully towards the mesh-free fit.

See also

rational.coefficients.wl2(), rspde.xmin()

Examples

x <- seq(from = 0, to = 1, length.out = 101)
op <- matern.operators(
  loc_mesh = x, nu = 0.4, range = 0.2, sigma = 1, d = 1, m = 2,
  parameterization = "matern", type = "operator",
  type_rational_approximation = "wl2"
)
op <- update_rational_coefficients(op)