Frequentist Prediction Sets for Species Abundance using Indirect Information

Citizen science databases that consist of volunteer-led sampling efforts of species communities are relied on as essential sources of data in ecology. Summarizing such data across counties with frequentist-valid prediction sets for each county provides an interpretable comparison across counties of varying size or composition. As citizen science data often feature unequal sampling efforts across a spatial domain, prediction sets constructed with indirect methods that share information across counties may be used to improve precision. In this article, we present a nonparametric framework to obtain precise prediction sets for a multinomial random sample based on indirect information that maintain frequentist coverage guarantees for each county. We detail a simple algorithm to obtain prediction sets for each county using indirect information where the computation time does not depend on the sample size and scales nicely with the number of species considered. The indirect information may be estimated by a proposed empirical Bayes procedure based on information from auxiliary data. Our approach makes inference for under-sampled counties more precise, while maintaining area-specific frequentist validity for each county. Our method is used to provide a useful description of avian species abundance in North Carolina, USA based on citizen science data from the eBird database.