Adjusting for Imperfect Detection in Block Kriging and in a Bayesian Hierarchical Model
A finite population version of block kriging (FPBK) that assumes perfect detection is routinely used to estimate moose abundance in Alaska. Because moose are less readily detected on ground without snow, declining snowfall in recent years makes the assumption of perfect detection less reasonable. In response, biologists have started to collect additional data on detection. We consider a frequentist adjustment to the FPBK predictor as well as a Bayesian hierarchical model (BHM) to incorporate the possibility of imperfect detection. The frequentist model is a moment-based approach that requires an extension of Goodman’s (1960) result on the exact variance of the element-wise product of two random vectors. The benefits include a quick run time and being more easily implemented by wildlife biologists doing ecological surveys but one current drawback is an assumption of large counts on each site. The BHM is based on a binomial model for count data with detection estimated from external data and a spatial Poisson model for the unknown abundance. The BHM does not require a large count assumption but takes much longer to fit and demands that the user be familiar with Bayesian statistics and MCMC methods. Both estimators are applied to a moose survey in Togiak National Wildlife Refuge in Alaska to predict the moose population total in the region.