Standard geostatistical models used in abundance prediction assume that observed counts on each site are made without error. However, in some wildlife populations, assuming perfect detection of animal or plant counts is unrealistic.
We first construct an adjustment to a finite population block kriging (FPBK) estimator that allows the possibility of imperfect detection. The estimator makes use of sightability trials on radiocollared animals to estimate detection. Alternatively, we then build a Bayesian Hierarchical Model (BHM) to predict counts on unobserved sites with a layer in the hierarchical model that adjusts for the possibility of imperfect detection. We compare results from a Bayesian geostatistical model and a Bayesian CAR model, both with a latent spatial surface for the counts on the log-scale. Finally, the frequentist adjusted FPBK estimator uses the variance of the element-wise product of two random vectors. Estimating this variance matrix presents interesting challenges. We give and then compare via simulation a few candidate estimators for the true variance matrix of a Hadamard product of two random vectors.