A practical solution for linear inference computations

Summary. In this paper, we present a matrix form of Backus' theory of linear inference with multiple predictions. The Bayesian approach used by Backus allows the treatment of erroneous data and the imposition of the essential a priori bound on the model norm. We introduce a modification which involves translating the problem in accordance with an estimated model. Such a model may be known a priori or it may be constructed from the data. We are effectively able to bound the norm of all acceptable models from above and below and this results in more confining estimates of the predictions than provided by just an upper bound. In addition, the model construction approach allows us to make maximum use of the data in the inference computation. Our algorithm is robust and efficient, and estimates comparable to to those obtained from linear programming techniques have been achieved.