题目：” Approximate Bayesian Inference for Penalized Spline Models: Methods, Applications and Case Studies ”
摘要：Penalized splines are often attractive in handling the nonlinear effects in additive regression models because of their flexibility. In this talk, we first review classical nonparametric smoothing approaches in statistics, and discuss frequentist and Bayesian analysis of penalized spline regression. A new statistical technique, known as integrated nested Laplace approximation (INLA), is then applied to implement approximate Bayesian inference for a large class of penalized spline models. It is shown that INLA provides not only accurate but also computationally fast approximations to the posterior marginals of regression parameters. A variety of applications and case studies, including functional data analysis, generalized semiparametric mixed models, and spatial econometrics, will be discussed by applying the penalized splines with INLA.