Corrected R-INLA CCD integration weights

Per-point design weights for a ccd_grid() used as nested-Laplace integration nodes. Implements the corrected R-INLA central-composite-design weights: the formula in Rue, Martino and Chopin (2009) has a typo, corrected by the R-INLA team to give a positive central weight. With m hyperparameters, np design points and standardized scaling f0, every non-centre point gets $$w = 1 / ((np - 1)(1 + e^{-m f0^2 / 2}(f0^2 - 1)))$$ and the centre point gets \(w_0 = 1 - (np - 1) w\). Used as \(\Delta_k\): the integration weight of node \(k\) is \(\Delta_k \exp(\log\,\mathrm{marginal}_k)\), renormalized. On a standardized (whitened) hyperparameter posterior these reproduce the Gaussian moments exactly.

Usage

ccd_weights(ccd)

Arguments

ccd

A ccd_grid() result. The standardized scaling is recovered as f0 = ccd$f_0 / sqrt(m): a ccd_grid(m, f_0 = sqrt(m) * f0) design places the factorial corners at +/- f0, matching the INLA convention (f0 = 1.1 is the INLA default).

Value

Numeric vector of length ccd$n_points: the design weight for each point (the centre weight w0 for the central point, w otherwise).

See also

ccd_grid(), ccd_to_theta().