Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

A general-purpose engine for fitting Bayesian hierarchical models with spatial fields, temporal effects, spatially varying coefficients, and multiple inference backends. Scalable spatial structure includes Hilbert space approximate Gaussian processes (HSGP; Riutort-Mayol et al. 2023 ), nearest-neighbor Gaussian processes (NNGP; Datta et al. 2016 ), intrinsic conditional autoregressive models (ICAR; Besag, York, and Mollie 1991 ), the reparameterized Besag-York-Mollie model (BYM2; Riebler et al. 2016 ), and stochastic partial differential equation fields (SPDE; Lindgren, Rue, and Lindstrom 2011 ). Temporal structure covers random walks, autoregressive processes, and Gaussian processes. Inference is tiered by correctness guarantee: exact Hamiltonian Monte Carlo with the No-U-Turn sampler, Laplace and nested Laplace approximations with hyperparameter integration (Rue, Martino, and Chopin 2009 ), and variational inference. Model-specific packages plug observation likelihoods into the engine through a templated C++ callback interface.