Map standardised CCD coordinates to physical hyperparameters

Converts standardised CCD z-coordinates (in \(\mathbb{R}^k\)) to physical hyperparameters \(\theta\) via the affine map \(\theta = \hat\theta + L \cdot z\) with optional log-scale transform per component. L is typically a Cholesky factor of the negative Hessian inverse evaluated at the (working) mode \(\hat\theta\) – i.e. it scales z to one posterior standard deviation per axis.

Usage

ccd_to_theta(z, theta_hat, L, log_scale = FALSE)

Arguments

z

Matrix [n_points x k] of standardised coordinates from ccd_grid().

theta_hat

Numeric vector of length k: centre of the design, in either physical or log-space (per log_scale).

L

Numeric [k x k] matrix: scale/rotation applied to z. Pass diag(sd) for a diagonal axis-aligned grid where sd is the per-axis posterior SD; pass a Cholesky factor to capture correlations between hyperparameters.

log_scale

Logical (or logical vector of length k). If TRUE for component j, theta_hat[j] and column j of the affine transform live on log-scale and are exponentiated afterward (useful for positive parameters like tau). Default FALSE everywhere.

Value

Numeric matrix [n_points x k] of physical theta-values.