Bayesian Analysis of Extreme Values Using Splines in Generalized Mixed Model

Modeling of extreme responses in presence nonlinear, temporal, spatial and interaction effects can be accomplished with mixed models. In addition, smoothing spline through mixed model and Bayesian approach together provide convenient framework for inference of extreme values. In this article, by representing as a mixed model, smoothing spline is used to assess nonlinear covariate effect on extreme values. For this reason, we assume that extreme responses given covariates and random effects are independent with generalized extreme value distribution. Then by using MCMC techniques in Bayesian framework, location parameter of distribution is estimated as a smooth function of covariates. Finally, the proposed model is employed to model the extreme values of ozone data.