INLA

Compared with MCMC-based flexible joint models, INLA was faster and avoided sampling convergence problems. The model is formulated as a latent Gaussian model so that INLA can approximate posterior marginals deterministically. The final model treats scaling weights evaluated from preliminary posterior expectations as deterministic while keeping the latent process jointly estimated. An internal calibration step keeps the non-linear association compatible with INLA's latent Gaussian structure. The paper proposes using INLA to address computational and software barriers in flexible Bayesian joint models.