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RBesT (version 1.11-0)

integrate_gauss_quadrature: 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

Arguments

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"