Gaussian process forecasting of sparse ecological time series

Ecological time series are often unevenly sampled in time. That is, because the sampling processes used are resource intensive, data may be collected infrequently, or with adaptive frequencies triggered by presence of a target variable. When the data are irregularly spaced, standard time series methods may not be directly applicable. Instead, approaches that take inspiration from linear regression (LR) may be appropriate. In this paper, we explore flexible, nonparametric Gaussian Process (GP) models as tools for producing forecasts of unevenly sampled observations. Our example is data on abundances of nymphal Amblyomma americanum from nine locations spread across the eastern United States, collected by NEON. The data exhibit highly variable sampling regimes and abundance levels across sites and time. We implement two versions of GPs to forecast tick abundance and benchmark them models against LR approaches. Both GPs are able to capture population patterns without the need for forecasting additional drivers, such as temperature, or specifying a specific relationship between the response and predictors. Further, our Heteroskedastic Gaussian Process (HetGP) model allows for flexible bounds and yields improved uncertainty quantification. We find that GP models provide an effective method to forecast irregularly sampled populations at short to intermediate time scales.