ABSTRACT
This chapter shows how to make Bayesian inference on these models using integrated nested Laplace approximations. In the frequentist paradigm, the additive models can be taken as a form of nonparametric regression, and be fitted using the backfitting algorithm. The chapter represents the smooth arbitrary functions with a family of spline basis functions, and then estimates the function coefficients based on the penalized likelihood method. The Bayesian backfitting algorithm combined with Markov chain Monte Carlo simulations is often used to sample the marginal posterior distributions. The authors believe it is because the distribution of rents is skewed to the right, and the normality assumption used in the model is not quite appropriate. But, generally speaking, the model provides reasonable results. A generalized additive model, like the additive model, can be fitted using the mgcv and the gam packages, but with different approaches. Bell studied result of multiple-level thoracic and lumbar laminectomy, a corrective spinal surgery commonly performed on children.
