An exponential–gamma mixture model for extreme Santa Ana winds

We analyze the behavior of extreme winds occurring in Southern California during the Santa Ana wind season using a latent mixture model. This mixture representation is formulated as a hierarchical Bayesian model and fit using Markov chain Monte Carlo. The two-stage model results in generalized Pareto margins for exceedances and generates temporal dependence through a latent Markov process. This construction induces asymptotic independence in the response, while allowing for dependence at extreme, but subasymptotic, levels. We compare this model with a frequentist analogue where inference is performed via maximum pairwise likelihood. We use interval censoring to account for data quantization and estimate the extremal index and probabilities of multiday occurrences of extreme Santa Ana winds over a range of high thresholds.