Horvitz-Thompson-like estimation with distance-based detection probabilities for circular plot sampling of forests

In circular plot sampling, trees within a given distance from the sample plot location constitute a sample, which is used to infer characteristics of interest for the forest area. If the sample is collected using a technical device located at the sampling point, eg, a terrestrial laser scanner, all trees of the sample plot cannot be observed because they hide behind each other. We propose a Horvitz-Thompson-like estimator with distance-based detection probabilities derived from stochastic geometry for estimation of population totals such as stem density and basal area in such situation. We show that our estimator is unbiased for Poisson forests and give estimates of variance and approximate confidence intervals for the estimator, unlike any previous methods. We compare the estimator to two previously published benchmark methods. The comparison is done through a simulation study where several plots are simulated either from field measured data or different marked point processes. The simulations show that the estimator produces lower or comparable error values than the other methods. In the sample plots based on the field measured data, the bias is relatively small-relative mean of errors for stem density, for example, varying from 0.3% to 2.2%, depending on the detection condition. The empirical coverage probabilities of the approximate confidence intervals are either similar to the nominal levels or conservative in these sample plots.