Modelling spatial zero-inflated continuous data with an exponentially compound Poisson process

A parsimonious model is presented as an alternative to delta approaches to modelling zero-inflated continuous data. The data model relies on an exponentially compound Poisson process, also called the law of leaks (LOL). It represents the process of sampling resources that are spatially distributed as Poisson distributed patches, each containing a certain quantity of biomass drawn from an exponential distribution. In an application of the LOL, two latent structures are proposed to account for spatial dependencies between zero values at different scales within a hierarchical Bayesian framework. The LOL is compared to the delta-gamma (Delta I) distribution using bottom-trawl survey data. Results of this case study emphasize that the LOL provides slightly better fits to learning samples with a very high proportion of zero values and small strictly positive abundance data. Additionally, it offers better predictions of validation samples.