Betting on residual life : The caveats of conditioning

Assessing conditionals based on any specified probability model is straightforward and unique when the conditioning event is in the subjunctive mood; that is, supposing that the conditioning event were to occur. The matter becomes problematic, however, when the conditioning event actually does occur as observed data, and thus becomes a reality. We illustrate this point by considering a commonly occurring scenario in the actuarial sciences, engineering reliability, survival analysis, and in general, any type of an activity that involves filtering. We argue that there could be more than one way to bet on residual life. Our message is that it is the likelihood-not Bayes' Law-which is the tail that wags the dog! This paper should appeal to both probabilists and statisticians who are interested in foundational issues. It has been written to honour Richard Johnson whose Editorship of Statistics and Probability Letters has provided a platform for dialogue between probabilists, statisticians, and those who strive to be both. © 2007 Elsevier B.V. All rights reserved.