Summary 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. 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. 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. 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. 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.

This proceedings paper is the first in a series of three papers developing mathematical models for the complex relationship between pain and the sleep-wake cycle. Here, we briefly review what is known about the relationship between pain and the sleep-wake cycle in humans and laboratory rodents in an effort to identify constraints for the models. While it is well accepted that sleep behavior is regulated by a daily (circadian) timekeeping system and homeostatic sleep drive, the joint modulation of these two primary biological processes on pain sensitivity has not been considered. Under experimental conditions, pain sensitivity varies across the 24 h day, with highest sensitivity occurring during the evening in humans. Pain sensitivity is also modulated by sleep behavior, with pain sensitivity increasing in response to the build up of homeostatic sleep pressure following sleep deprivation or sleep disruption. To explore the interaction between these two biological pro- The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/098269 doi: bioRxiv preprint first posted online Jan. 9, 2017; 2 Hagenauer, Crodelle, Piltz, Toporikova, Ferguson and Booth cesses using modeling, we first compare the magnitude of their effects across a variety of experimental pain studies in humans. To do this comparison, we normalize the results from experimental pain studies relative to the range of physiologicallymeaningful stimulation levels. Following this normalization, we find that the estimated impact of the daily rhythm and of sleep deprivation on experimental pain measurements is surprisingly consistent across different pain modalities. We also review evidence documenting the impact of circadian rhythms and sleep deprivation on the neural circuitry in the spinal cord underlying pain sensation. The characterization of sleep-dependent and circadian influences on pain sensitivity in this review paper is used to develop and constrain the mathematical models introduced in the two companion articles.

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