Building Hierarchical Models with an Integrated Likelihood for Distance Sampling

C. S. Oedekoven, S. T. Buckland, M. L. Mackenzie, R. King, K. O. Evans and L. W Burger, Jr.

University of St. Andrews and Mississippi State University


Few distance sampling studies exist that use Bayesian analytical methods. These studies focus on line-transects and use the half-normal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function which may also include covariates affecting detection probabilities. The approach uses an integrated likelihood which incorporates the detection and density models. For the latter, densities are related to covariates in a log-linear mixed effects Poisson model. We use a Metropolis Hastings algorithm for updating parameters and a reversible jump algorithm to include mo0del selection for both the detection function and density models to allow for model uncertainty. The number of possible models included in the model selection depends on the number of covariates available and the detection function considered. The approach is applied to a case study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and density models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach reveled better precision estimates even though it does not condition on a known detection function for the density model.


hazard-rate detection function; heterogeneity in detection probabilities; Metropolis Hastings update; point transect sampling; RJMCMC