The prediction of outstanding claims amounts in non-life insurance is, by its very nature, highly speculative. Partially because of this and partially because of the variety of features suggested by various researchers for possible inclusion in the structure of the underlying prediction model, the past two decades have seen a proliferation of methodologies for making such predictions. Specific details of these developments are contained in a comprehensive and highly detailed survey conducted by Taylor (1986) in which a taxonomy of methods is established. One feature common to all of these methods is the utilization of current and past records of claims amounts—invariably in the form of the familiar so-called runoff triangle or a variant thereof—to calibrate the proposed prediction model before use. Prudence dictates that diagnostic checks should then be made to establish whether or not the data are supportive of the structure imparted to the prediction model before use, a feature which apart from some notable exceptions including Zehnwirth (1985) and Taylor (1983), is not always emphasized in the literature.