Continuous-space occupancy models.

Occupancy models are used to infer species distributions over large spatial extents while accounting for imperfect detection. Current approaches, however, are unable to model species occurrence over continuous spatial domains while accounting for the discrete spatial domain of the observed data. We develop a new class of spatial occupancy models that embeds a change of spatial support between the observed data and occurrence process. We use a clipped Gaussian process to represent species occurrence in continuous space, which can provide inferences at a finer resolution than the observed occupancy data. Our approach is beneficial because it allows for more realistic models of species occurrence, can account for species occurring in only a portion of a surveyed site, and can relate detection probabilities to these within-site occurrence proportions. We show how our model can be fit using Bayesian methods and develop a computationally efficient MCMC algorithm. In particular, we rely on a Vecchia approximation to implement the spatial Gaussian process describing species occurrence and develop a surrogate data approach for jointly updating the spatial terms and spatial covariance parameters. We demonstrate our model using simulated data and compare our approach to alternative spatial occupancy models. We also use our model to analyze ovenbird occurrence data collected in New Hampshire, USA.