Model-based entropy estimation for data with covariates and dependence structures

Abstract

Entropy is widely used in ecological and environmental studies, where data often present complex interactions. Difficulties arise in linking entropy to available covariates or data dependence structures, thus, all existing entropy estimators assume independence. To overcome this limit, we take a Bayesian model-based approach which focuses on estimating the probabilities that compose the index, accounting for any data dependence and correlation. An estimate of entropy can be constructed from the model fitted values, returning an observation-specific measure of entropy rather than an overall index. This way, the latent heterogeneity of the system can be represented by a curve in time or a surface in space, according to the characteristics of the survey study at hand. An empirical study illustrates the flexibility and interpretability of our results over temporally and spatially correlated data. An application is presented about the biodiversity of spatially structured rainforest tree data.