A Discipline for the Avoidance of Unnecessary Assumptions

Although unnecessary assumptions are something we all try to avoid, advice on how to do so is much harder to come by than admonition. The most widely quoted dictum on the subject, often referred to by writers on philosophy as "Ockham's razor" and attributed generally to William of Ockharn, states "Entianon sunt multiplicanda praeter necessitatem". (Entities are not to be multiplied without necessity.) As pointed out in reference [1], however, the authenticity of this attribution is questionable. The same reference mentions Newton's essentially similar statement in his Principia Mathematica of 1726. Hume [3] is credited by Tribus [2c] with pointing out in 1740 that the problem of statistical inference is to find an assignment of probabilities that "uses the available information and leaves the mind unbiased with respect to what is not known." The difficulty is that often our data are incomplete and we do not know how to create an intelligible interpretation without filling in some gaps. Assumptions, like sin, are much more easily condemned than avoided. In the author's opinion, important results have been achieved in recent years toward solving the problem of how best to utilize data that might heretofore have been regarded as inadequate. The approach taken and the relevance of this work to certain actuarial problems will now be discussed.