Comment on Article by Page and Quintana

Page and Quintana (2016) introduce the novel methodology of spatial product partition models in order to explicitly model the partitioning of spatial locations, with the aim of balancing local and global spatial dependence. Here we first discuss Gibbs-type partitions and their connection to exchangeable product partition models and their possible use as building blocks of spatial product partition models. Then, adopting the viewpoint of extreme value theory, we focus on two approaches for modeling spatial extremes, namely hierarchical modeling based on a latent stochastic process and modeling based on max-stable processes. Additional insights and interesting findings may arise by developing the approach of Page and Quintana (2016) along these lines.