Occupancy models for data with false positive and false negative errors and heterogeneity across sites and surveys

1. False positive detections, such as species misidentifications, occur in ecological data, although many models do not account for them. Consequently, these models are expected to generate biased inference. 2. The main challenge in an analysis of data with false positives is to distinguish false positive and false negative processes while modelling realistic levels of heterogeneity in occupancy and detection probabilities without restrictive assumptions about parameter spaces. 3. Building on previous attempts to account for false positive and false negative detections in occupancy models, we present hierarchical Bayesian models that utilize a subset of data with either confirmed detections of a species' presence (CP model) or both confirmed presences and confirmed absences (CACP model). We demonstrate that our models overcome the challenges associated with false positive data by evaluating model performance in Monte Carlo simulations of a variety of scenarios. Our models also have the ability to improve inference by incorporating previous knowledge through informative priors. 4. We describe an example application of the CP model to quantify the relationship between songbird occupancy and residential development, plus we provide instructions for ecologists to use the CACP and CP models in their own research. 5. Monte Carlo simulation results indicated that, when data contained false positive detections, the CACP and CP models generated more accurate and precise posterior probability distributions than a model that assumed data did not have false positive errors. For the scenarios we expect to be most generally applicable, those with heterogeneity in occupancy and detection, the CACP and CP models generated essentially unbiased posterior occupancy probabilities. The CACP model with vague priors generated unbiased posterior distributions for covariate coefficients. The CP model generated unbiased posterior distributions for covariate coefficients with vague or informative priors, depending on the function relating covariates to occupancy probabilities. We conclude that the CACP and CP models generate accurate inference in situations with false positive data for which previous models were not suitable.