Preferential sampling for presence/absence data and for fusion of presence/absence data with presence-only data

Presence/absence data and presence-only data are the two customary sources for learning about species distributions over a region. We present an ambitious agenda with regard to such data. We illuminate the fundamental modeling differences between the two types of data. Most simply, locations are considered as fixed under presence/absence data; locations are random under presence-only data. The definition of \"probability of presence\" is incompatible between the two. So, we take issue with modeling strategies in the literature which ignore this incom-patibility, which assume that presence/absence modeling can be induced from presence-only specifications and therefore, that fusion of presence-only and presence/absence data sources is routine.\n\nWe argue that presence/absence data should be modeled at point level. That is, we need to specify a surface which provides the probability of presence at any location in the region. A realization from this surface is a binary map yielding the results of Bernoulli trials across all locations; this surface is only partially observed. Presence-only data should be modeled as a (partially observed) point pattern, arising from a random number of individuals at random locations, driven by specification of an intensity function. There is no notion of Bernoulli trials; events are associated with areas.\n\nWe further argue that, with just presence/absence data, preferential sampling, using a shared process perspective, can improve our estimated presence/absence surface and prediction of presence. We also argue that preferential sampling can enable a probabilistically coherent fusion of the two data types.\n\nWe illustrate with two real datasets, one presence/absence, one presence-only for invasive species presence in New England in the United States. We demonstrate that potential bias in sampling locations can affect inference with regard to presence/absence and show that in-ference can be improved with preferential sampling ideas. We also provide a probabilistically coherent fusion of the two datasets to again improve inference with regard to presence/absence.\n\nThe importance of our work is to provide more careful modeling when studying species distributions. Ignoring incompatibility between data types and offering incoherent modeling specifications implies invalid inference; the community should benefit from this recognition.