Despite the popularity of random forests (RF) as a prediction algorithm, methods for constructing confidence intervals for population means using this technique are still only sparsely reported. For two regional study areas (Spain and Norway) RF was used to predict forest volume or aboveground biomass using remotely sensed auxiliary data obtained from multiple sensors. Additionally, the changes per unit area of these forest attributes were estimated using indirect and direct methods. Multiple inferential frameworks have attracted increased recent attention for estimating the variances required for confidence intervals. For this study, three different statistical frameworks, design-based expansion, model-assisted and model-based estimators, were used for estimating population parameters and their variances. Pairs and wild bootstrapping approaches at different levels were compared for estimating the variances of the model-based estimates of the population means, as well as for mapping the uncertainty of the change predictions. The RF models accurately represented the relationship between the response and remotely sensed predictor variables, resulting in increased precision for estimates of the population means relative to design-based expansion estimates. Standard errors based on pairs bootstrapping within or internal to RF were considerably larger than standard errors based on both pairs and wild external bootstrapping of the entire RF algorithm. Pairs and wild external bootstrapping produced similar standard errors, but wild bootstrapping better mimicked the original structure of the sample data and better preserved the ranges of the predictor variables.

Forest/non-forest and forest species maps are often used by forest inventory programs in the forest estimation process. For example, some inventory programs establish field plots only on lands corresponding to the forest portion of a forest/non-forest map and use species-specific area estimates obtained from those maps to support the estimation of species-specific volume (V) totals. Despite the general use of these maps, the effects of their uncertainties are commonly ignored with the result that estimates might be unreliable. The goal of this study is to estimate the effects of the uncertainty of forest species maps used in the sampling and estimation processes. Random forest (RF) per-pixel predictions were used with model-based inference to estimate V per unit area for the six main forest species of La Rioja, Spain. RF models for predicting V were constructed using field plot information from the Spanish National Forest Inventory and airborne laser scanning data. To limit the prediction of V to pixels classified as one of the main forest species assessed, a forest species map was constructed using Landsat and auxiliary information. Bootstrapping techniques were implemented to estimate the total uncertainty of the V estimates and accommodated both the effects of uncertainty in the Landsat forest species map and the effects of plot-to-plot sampling variability on training data used to construct the RF V models. Standard errors of species-specific total V estimates increased from 2–9% to 3–22% when the effects of map uncertainty were incorporated into the uncertainty assessment. The workflow achieved satisfactory results and revealed that the effects of map uncertainty are not negligible, especially for open-grown and less frequently occurring forest species for which greater variability was evident in the mapping and estimation process. The effects of forest map uncertainty are greater for species-specific area estimation than for the selection of field plots used to calibrate the RF model. Additional research to generalize the conclusions beyond Mediterranean to other forest environments is recommended.