A zero-inflated hidden semi-Markov model with covariate-dependent sojourn parameters for analysing marine data in the Venice lagoon

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.