Conservative Rules for Predictive Inference with Incomplete Data
Marco Zaffalon · 2005
This paper addresses the following question: how should we update our beliefs after observing some incomplete data, in order to make credible predictions about new, and possibly incomplete, data? There may be several answers to this question according to the model of the process that creates the incompleteness. This paper develops a rigor-ous modelling framework that makes it clear the condi-tions that justify the different answers; and, on this basis, it derives a new conditioning rule for predictive inference to be used in a wide range of states of knowledge about the incompleteness process, including near-ignorance, which, surprisingly, does not seem to have received attention so far. Such a case is instead particularly important, as mod-elling incompleteness processes can be highly impractical, and because there are limitations to statistical inference with incomplete data: it is generally not possible to learn how incompleteness processes work by using the available data; and it may not be possible, as the paper shows, to measure empirically the quality of the predictions. Yet, these depend heavily on the assumptions made.