Geometric overdispersion facilitates the integration of ecological data

Statistical data integration facilitates inference based on the variety of data prevalent in ecology. In particular, integrated distribution models (IDMs) have been proposed for inferring spatial patterns in abundance using combinations of noisy count, presence–absence and presence–only data. Obtaining posterior inference from these models is challenging because most optimized software only pertains to a single data type or perfectly observed counts and more general approaches are computationally burdensome. We propose an efficient modelling framework for the joint analysis of multiple datasets. Our framework assumes that each data type arises from the same latent spatial process and allows for unique observational bias and uncertainty. Our implementation is computationally tractable because we model abundance as geometric random variables, which facilitates Markov chain Monte Carlo algorithms with Gibbs updates using Pólya-Gamma augmentation. In a simulation study, we show that our geometric model can provide a useful approximation to Poisson-based IDMs and improves posterior inference for spatial variation in abundance, especially for overdispersed count data. Even for moderately sized datasets (i.e. (Formula presented.) sites), our approach is nearly 100 times more computationally efficient than Poisson IDMs implemented with Stan. Our approach has computational efficiency similar to variational inference, but results in less bias. We demonstrate the flexibility and scalability of the geometric-based IDM in case studies of Turdus migratorius and Salvelinus fontinalis abundance. Our contribution complements ongoing developments in integrated ecological models by providing a fast and flexible framework for joint inference on high-dimensional latent effects. We further evaluate the relative performance of Poisson, negative binomial and geometric models for estimating covariate associations and spatial variation in abundance.