Hierarchical-Generalized Pareto Model for Estimation of Unhealthy Air Pollution Index

摘要

A common way of modeling the exceedance of air pollution index (API) data is to utilize the generalized Pareto distribution (GPD). The marginal GPD model is a good method for describing unhealthy API data. However, for data with multiple locations, integrating the information of GDP models from each location with a hierarchical model (HM) will provide a better result. In this study, a hierarchical-generalized Pareto model (HM-GPD) is used to integrate the information about location and seasonal effects from the marginal GPD models of hourly API exceedance data, along with the information of serial dependence at each location. The accuracy of inferences at a single site and in each season was improved by employing a Gaussian model for the random effects; this model takes advantage of the climatological structure in the data. The temporal dependence was modeled by using first-order Markov chains. This step was performed by operating the posterior draws from HM-GPD to transform the marginal models for each site to unit Frechet by using the Markov chain model likelihood. Overall, the parameters estimated from the HM-GPD are able to provide precise estimation of the return levels for each site.