Modelling environmental DNA data; Bayesian variable selection accounting for false positive and false negative errors

Environmental DNA is a survey tool with rapidly expanding applications for assessing the presence of a species at surveyed sites. Environmental DNA methodology is known to be prone to false negative and false positive errors at the data collection and laboratory analysis stages. Existing models for environmental DNA data require augmentation with additional sources of information to overcome identifiability issues of the likelihood function and do not account for environmental covariates that predict the probability of species presence or the probabilities of error. We present a novel Bayesian model for analysing environmental DNA data by proposing informative prior distributions for logistic regression coefficients that enable us to overcome parameter identifiability, while performing efficient Bayesian variable selection. Our methodology does not require the use of transdimensional algorithms and provides a general framework for performing Bayesian variable selection under informative prior distributions in logistic regression models.