A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences

Motivated by studies of wildfire seasonality, we propose a nonhomogeneous hidden Markov random field to model the spatial distribution of georeferenced fire occurrences during the year, by representing occurrence times as circular data. The model is based on a mixture of Kato–Jones circular densities, whose parameters vary across space according to a latent nonhomogeneous Potts model, modulated by georeferenced covariates. It allows us to segment fire occurrences according to a finite number of latent classes that represent the conditional distributions of the data under specific periods of the year, simultaneously accounting for unobserved heterogeneity and spatial autocorrelation. Further, it parsimoniously accommodates specific features of wildfire occurrence data such as multimodality, skewness, and kurtosis. Due to the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods. It reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. The proposal is illustrated in a study of wildfire occurrences in the Iberian Peninsula during a decade.