We describe a statistical agent based model (SABM) for binary spatio-temporal data in which the occupancy of each cell evolves as a Bernoulli mixture of three mechanistically distinct processes:local persistence, anisotropic neighborhood dispersal, and long-distance dispersal. The model is embedded in a hierarchical Bayesian framework with conjugate Beta full-conditionals for the persistence and long-distance parameters and a Dirichlet prior on the directional dispersal kernel. A nonstationary extension links the dispersal kernel to a latent habitat-suitability surface through directional gradients of a Gaussian process. We show that, in the small-step regime, the Lagrangian recurrence for the dispersal kernel scales to a classical two dimensional advection diffusion partial differential equation whose drift and dispersion coefficients are the first and second moments of the dispersal probabilities. We provide an MCMC algorithm exploiting the exact full conditionals and demonstrate parameter recovery and PDE scaling agreement in a simulated example.
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