The bias of forecasts is a measure of the tendency of a model to systematically under- or over-predict71. The bias of a set of predictions I^jt at time t at location j is defined as

where the mean is taken across the N draws. H(x) is the Heaviside step function defined as

The above formulation can better be understood by considering the following extreme scenarios. If every projected value I^jt is greater than the observed value Ijt, then the Heaviside function is 1 for all i = 1, 2, …N, and meanHI^jtIjt is 1. The bias for a model that always over-predicts is therefore 1. On the other hand, if the model systematically under-predicts, then meanHI^jtIjt is 0 and the bias is -1. For a model for which all predictions match the observed values exactly, the bias is 0.

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