Data from: Abundance estimation with sightability data: a Bayesian data augmentation approach

1.Steinhorst&Samuel(1989)showedhowlogistic-regressionmodels,fit to detection data collected from radiocollaredanimals,can be used to estimate and adjust forvisibility bias in wildlife population surveys.Population abundance is estimated using a modified Horvitz Thompson(mHT) estimator in which counts of observed animal groups are divided by their estimated inclusion probabilities (determinedbyplot level sampling probabilities and detection probabilities estimated from radiocollaredindividuals).The sampling distribution of the mHT estimator is typically right skewed,and statistica linference relies on asymptotic theory that may not b eappropriate with small samples.2.We develop an alternative, Bayesian model based approach which we apply to data collected from moose (Alce salces) in Minnesota. We model detection probabilities as a function of visual obstruction, informed by data from 124 sightability trials involving radiocollared moose.These sightability data,along with counts of moose from a stratified random sample of aerial plots,are used to estimate moose abundance in2006 and 2007 and the log rate of change between the two years. 3.Unlike traditional design-based estimators,model based estimators require assumptions regarding stratum specific distributions of the detection covariates,the number of animal groups per plot,and the number of animals per animal group.We demonstrate numerical and graphical methods for assessing the validity of these assumption and compare two different models for the distribution of the number of animal groups per plot,a beta-binomial model and a logistic-t -model 4.Estimates of the log-rate of change (95%CI) between 2006 and 2007 were-0.21(-0.53,0.12),-0.24(-0.64,0.16),and-0.25(-0.64,0.15) for the beta-binomialmodel,logistic-t-model,and mHT estimator,respectively.Plots of posterior-predictive distributions and goodness-of-fit measures both suggest the beta-binomial model provides a better fit to the data. 5.The Bayesian frame work offers many inferential advantages,including the ability to incorporate prior information and perform exact inference with small samples.More importantly,themodel-based approach provides additional flexibility when designing and analyzing multi-year surveys (e.g.,rotational sampling designs could be used to focus sampling effort in important areas,and random effects could be used to share information across years)