  Spatially correlated data with an excess of zeros, usually referred to as
zero-inflated spatial data, arise in many disciplines. Examples include count
data, for instance, abundance (or lack thereof) of animal species and disease
counts, as well as semi-continuous data like observed precipitation. Spatial
two-part models are a flexible class of models for such data. Fitting two-part
models can be computationally expensive for large data due to high-dimensional
dependent latent variables, costly matrix operations, and slow mixing Markov
chains. We describe a flexible, computationally efficient approach for modeling
large zero-inflated spatial data using the projection-based intrinsic
conditional autoregression (PICAR) framework. We study our approach, which we
call PICAR-Z, through extensive simulation studies and two environmental data
sets. Our results suggest that PICAR-Z provides accurate predictions while
remaining computationally efficient. An important goal of our work is to allow
researchers who are not experts in computation to easily build computationally
efficient extensions to zero-inflated spatial models; this also allows for a
more thorough exploration of modeling choices in two-part models than was
previously possible. We show that PICAR-Z is easy to implement and extend in
popular probabilistic programming languages such as nimble and stan.
