Accuracy and Precision for Remote Sensing Applications of Nonlinear Model-Based Inference

In a forest inventory context, estimation for small areas and for remote and inaccessible regions may be problematic using traditional probability- or design-based inference because acquisition of sufficiently large samples to satisfy precision requirements is financially and/or logistically difficult. These problems can often be partially alleviated for inventory applications by enhancing inferences using models and remotely sensed independent variables. However, estimates obtained using probability-based, model-assisted estimators may still suffer detrimental effects as the result of small sample sizes. Model-based inference has the potential to alleviate these problems because precision is affected by other factors such as model specification. Nevertheless, model specification in the form of selection of independent variables often focuses exclusively on quality of fit with little consideration given to the precision of estimates of areal population parameters. Model-based inference is illustrated for two forest inventory applications, estimation of mean proportion forest area using Landsat-based independent variables for a study area in the USA and estimation of mean growing stock volume per unit area using lidar-based independent variables for a study area in Norway. Variations of a nonlinear logistic regression model are used for both applications. The results indicate selection of subsets of remotely sensed independent variables to maximize precision had negligible effects on the quality of fit of the models to the data and on estimates of means but substantial proportional beneficial effects on precision.