Why ecosystem characteristics predicted from remotely sensed data are unbiased and biased at the same time – and how this affects applications

Remotely sensed data are frequently used for predicting and mapping ecosystem characteristics, and spatially explicit wall-to-wall information is sometimes proposed as the best possible source of information for decision-making. However, wall-to-wall information typically relies on model-based prediction, and several features of model-based prediction should be understood before extensively relying on this type of information. One such feature is that model-based predictors can be considered both unbiased and biased at the same time, which has important implications in several areas of application. In this discussion paper, we first describe the conventional model-unbiasedness paradigm that underpins most prediction techniques using remotely sensed (or other) auxiliary data. From this point of view, model-based predictors are typically unbiased. Secondly, we show that for specific domains, identified based on their true values, the same model-based predictors can be considered biased, and sometimes severely so.

We suggest distinguishing between conventional model-bias, defined in the statistical literature as the difference between the expected value of a predictor and the expected value of the quantity being predicted, and design-bias of model-based estimators, defined as the difference between the expected value of a model-based estimator and the true value of the quantity being predicted. We show that model-based estimators (or predictors) are typically design-biased, and that there is a trend in the design-bias from overestimating small true values to underestimating large true values. Further, we give examples of applications where this is important to acknowledge and to potentially make adjustments to correct for the design-bias trend. We argue that relying entirely on conventional model-unbiasedness may lead to mistakes in several areas of application that use predictions from remotely sensed data.