A Closer Look at Statistical Uncertainty in Forest Ecosystem Surveys Using Remotely Sensed Data and Model-Based Inference

Many forest ecosystem surveys use remotely sensed data and model-based inference. Assessing uncertainties in connec­tion with such surveys is far from trivial. Focusing on continuous study variables, such as biomass, we first motivate why the mean square error (MSE) of predictors of population quantities of interest is a relevant measure of overall uncertainty. Secondly, we separate the MSE into four components involving (i) the variance of the predictor, (ii) the model-bias of the predictor, (iii) the variance of the true value of the quantity predicted, and (iv) the cova­riance between the predictor and the true value, and show how the different compo­nents can be estimated. Thirdly, based on simulations mimicking conditions in Eastern Africa and Western USA, we assess which components are influential in different survey contexts. Our findings show that using the variance of a predictor, alone, as a measure of uncertainty is a fair approxi­mation if the study area is large and if the model linking remotely sensed data with reference data is adequately specified and estimated. However, we identify substantial risks of underestimating the MSE if models are extrapolated beyond conditions for which they were calibrated, in which case predictors were found to be severely model-biased. The remaining terms contributed differently in large-area surveys compared to small-area surveys. In small-area surveys, the MSE compo­nent (iii) is the dominating part. An interesting observation was that the MSE of a predictor is sometimes smaller than the variance of the predictor, due to the negative contribution from term (iv).