integrate_gauss_quadrature: Gaussian quadrature for mixture density integration

In RBesT: R Bayesian Evidence Synthesis Tools

Gaussian quadrature for mixture density integration

Description

Provides S3 methods for integrate_density and integrate_density_log that use Gaussian quadrature matched to the mixture family:

• normMix: Gauss-Hermite quadrature

• betaMix: Gauss-Jacobi quadrature

• gammaMix: Gauss-Laguerre quadrature

Details

The integration method is controlled by the global option RBesT.integrate_method (default "GQ"). Setting it to "adaptive" falls through to the default adaptive method.

Tolerance control is enabled by default: starting from RBesT.GQ_nodes nodes, the node count is repeatedly increased (by RBesT.GQ_node_growth, default doubling) until successive estimates agree within max(RBesT.GQ_abs_tol, RBesT.GQ_rel_tol * |I|). Setting RBesT.GQ_rel_tol to a non-finite or non-positive value (e.g. Inf) restores the legacy single-shot evaluation at RBesT.GQ_nodes nodes.

Relevant options (all consulted only on the "GQ" path):

• RBesT.GQ_nodes (default 20L) – starting node count

• RBesT.GQ_rel_tol (default 1e-4) – relative tolerance; a non-finite or non-positive value (e.g. Inf) disables refinement (single evaluation at RBesT.GQ_nodes)

• RBesT.GQ_abs_tol (default 1e-6) – absolute tolerance floor

• RBesT.GQ_max_nodes (default 240L) – refinement cap

• RBesT.GQ_node_growth (default 2) – node growth factor

• RBesT.GQ_on_nonconvergence (default "adaptive") – one of "adaptive" (fall through to adaptive integration), "warn", "error", "silent"

RBesT documentation built on Sept. 18, 2026, 5:06 p.m.