Probabilistic context neighborhood model for two-dimensional lattices

We present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov Random Field. In this model, the neighborhood structure has a fixed geometry but a variable radius, depending on the neighbors' values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependent neighborhood structure as a tree, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility.