How good are our best models? Jackknifing, bootstrapping, and earthquake depth

Abstract

Many techniques have been developed to extract a model from data. In general, these techniques are based on minimization of the misfit between measured data and predicted “data.” The model is connected to the predicted “data” by a physical theory. To know how good the model is, one must evaluate model variance. Since the data variance, or alternatively the misfit, is generally nonzero, model variance is generally nonzero. In many cases, the model is a linear function of the data, and model variance can be estimated by formally mapping the data variance to model space [e.g., Menke , 1984].