Adjusting a finite population block kriging estimator for imperfect detection

A finite population version of block kriging (FPBK) estimates a total or a mean when there is perfect detection of population units. However, many environmental datasets challenge the assumption of perfect detection. We consider two extensions of FPBK that incorporate imperfect detection. Spatial population estimator with detection: ratio then add (SPEDRA) adjusts observed counts by the estimated detection probability prior to spatial modeling. Spatial population estimator with detection: add then ratio (SPEDAR) uses spatial modeling on observed counts and then adjusts by mean detection probability. Unlike classical sampling approaches such as simple random sampling, SPEDRA and SPEDAR allow for spatial correlation among counts, and, being moment‐based, are less computationally intensive than a fully Bayesian model. Both SPEDRA and SPEDAR perform similarly in some simulation settings and give comparable estimates for a moose population total when applied to data from Togiak National Wildlife Refuge (AK). In settings where detection probability varies widely across sites, however, SPEDRA outperforms SPEDAR in reducing root mean square prediction error. We recommend SPEDRA in surveys with imperfect detection because it is more theoretically sound and generally performs better.