Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines

Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between covariates and response assumed to have conditional distribution in the exponential family. In this article, P-splines Laplace approximation coupled flexible fast approximate Bayesian inference GAMs. The proposed Laplace-P-spline model contributes development of new methodology explore posterior penalty space by considering deterministic grid-based strategy or Markov chain sampler, depending on number smooth terms predictor. Our approach has merit relying closed form analytical expressions gradient Hessian vector, which enables construct accurate pointwise credible set estimators latent field variables at relatively low computational budget even large components. Based upon simple Gaussian approximations posterior, suggested enjoys excellent properties. performance is confirmed through different simulation scenarios method illustrated two real datasets.