A zero-inflated hidden semi-Markov model with covariate-dependent sojourn parameters for analysing marine data in the Venice lagoon
本文提出一种带协变量的隐半马尔可夫模型，通过零膨胀泊松分布处理威尼斯泻湖洪水事件数据中的大量零值，并引入回归依赖的状态逗留参数，以更精确地捕捉环境风险状态与观测数据间的复杂关系。
Abstract This paper introduces a concomitant-variable hidden semi-Markov model tailored to analyse marine count data in the Venice lagoon. Our model targets acqua alta events, i.e. the exceedances of flooding limits, addressing the prevalent zero counts within the dataset through a fitted zero-inflated Poisson distribution. The data’s dynamics are attributed to a discrete set of hidden environmental risk states, evolving through time following a (nonhomogeneous) hidden semi-Markov chain. Furthermore, we extend the conventional hidden semi-Markov approach by introducing regression-dependent state-specific duration parameters, enhancing the model’s adaptability and precision in capturing real-world complexities. Our methodology hinges on the maximum-likelihood estimation, directly optimizing the log-likelihood function to infer the model’s parameters. Through the definition of this novel hidden semi-Markov model, we aim to offer a complete understanding of the intricate interplay between weather states, environmental variables, and the observed marine count data, thus contributing to a nuanced analysis of the Venice lagoon’s data.