Bayesian Treatment of Uncertain Data

Abstract

So far we have only analyzed cases where the observed data were known with certainty and completeness. Reality is messier in a number of ways with respect to observed data. For example, the number of binomial demands may not have been recorded and may have to be estimated. Similarly, the exposure time in the Poisson distribution may have to be estimated. One may not always be able to tell the exact number of failures that have occurred, because of imprecision in the failure criterion. When observing times at which failures occur (i.e., random durations), various types of censoring can occur. For example, a number of components may be placed in test, but the test is terminated before all the components have failed. This produces a set of observed data consisting of the recorded failure times for those components that have failed. For the components that did not fail before the test was terminated, all we know is that the failure time was longer than the duration of the test. As another example, in recording fire suppression times, the exact time of suppression may not be known; in some cases, all that may be available is an interval estimate (e.g., between 10 and 20 min). In this chapter, we will examine how to treat all of these cases, which we refer to generally as uncertain data.