Bayesian inference for generalized extreme value distribution with Gaussian copula dependence

Abstract: Dependent generalized extreme value (dGEV) models have attracted much attention due to the dependency structure that often appears in real datasets. To construct a dGEV model, a natural approach is to assume that some parameters in the model are time-varying. A previous study has shown that a dependent Gumbel process can be naturally incorporated into a GEV model. The model is a nonlinear state space model with a hidden state that follows a Markov process, with its innovation following a Gumbel distribution. Inference may be made for the model using Bayesian methods, sampling the hidden process from a mixture normal distribution, used to approximate the Gumbel distribution. Thus the response follows an approximate GEV model. We propose a new model in which each marginal distribution is an exact GEV distribution. We use a variable transformation to combine the marginal CDF of a Gumbel distribution with the standard normal copula. Then our model is a nonlinear state space model in which the hidden state equation is Gaussian. We analyze this model using Bayesian methods, and sample the elements of the state vector using particle Gibbs with ancestor sampling (PGAS). The PGAS algorithm turns out to be very efficient in solving nonlinear state space models. We also show our model is flexible enough to incorporate seasonality.