Constants linking the lengthscale to the approximate GP settings
Source:R/create.R
gp_approx_constants.RdConstants from Riutort-Mayol et al. (2023, Section 4.3.1)
doi:10.1007/s11222-022-10167-2
. With half-range S, boundary factor
c and m basis functions, lengthscales l are approximated accurately
when m >= m_factor * c * S / l and c >= c_factor * l / S (with
c >= 1.2). The paper does not cover Matern 1/2 (equivalently, the
Ornstein-Uhlenbeck kernel). Its m_factor is derived by repeating the
paper's simulation procedure (see the hsgp_m_c_relationship folder,
branch matern-half-m-c-relationship, of
https://github.com/sbfnk-bot/basis_functions_approach_to_GP).
The same procedure reproduced the squared exponential and Matern 3/2 and
5/2 constants to within 8-13%. Matern 1/2 is the roughest kernel, so it
needs the most basis functions. Its c_factor was not independently
validated and uses the Matern 3/2 value. The periodic kernel has no
boundary and needs m >= m_factor * S / l basis functions (Appendix B), so
its c_factor is NA.