Spatial Variation on Multiple Scales in Line Transect Data

A spatial model implemented in TMB was presented (mslt). The model was recently published in JASA (https://doi.org/10.1080/01621459.2025.2566422) . It treats whale sightings as arising from a thinned Cox process, with intensity driven by a latent Gaussian Markov random field (using the SPDE approach) and a two-state Markov-modulated Poisson process (MMPP). The SPDE component is intended to capture long-range spatial structures, wheras the MMPP accounts for short-range structure.

It was demonstrated that including the MMPP component typically increases the spatial correlation length of the SPDE component. This implies that the model can propagate the SPDE process further away from the transects when the MMPP is successfully included. The model jointly estimates the detection function, group intensity, and group size, ensuring that uncertainty is propagated automatically through the delta method implemented in TMB.