One posterior draw of the intensity surface

Generates a single posterior sample of $\lambda = \exp(z)$ under the Gaussian working model on the log scale with heteroscedastic variance $D$. It draws a GP prior realisation $\eta \sim \mathcal N(0, K)$, adds working-likelihood noise $\varepsilon \sim \mathcal N(0, D)$ on the observed log scale, solves $(S K S^\top + D)\alpha_{\sim} = (S\eta + \varepsilon) - y_{\text{work}}$, and returns $\exp(\eta - K S^\top \alpha_{\sim} + \mu_{\mathrm{infer}})$.

Usage

gp_draw(state, tol = 1e-06)

Arguments

state: A sampler state created by gp_build_state(), containing at least space_mat, time_mat, obs_idx, N, y_work, noise_var, kdiag_full, A_solve, and mu_infer. The vector layout is sites × times with time varying fastest.
tol: Convergence tolerance passed to the inner PCG solve.

Value

A numeric vector of length state$N containing one posterior draw of $\lambda$ in the same ordering as state$mu_infer.