Scenarios for Knowing

We shall next investigate a limited but interesting number of cases for which specific object-class laws p(ql9 . -, qM) are formed. Remarkably, in some cases the estimation principle (19) may itself be used to form p. In these cases we formally set all Xm = 0, because object class is defined independent of knowing the data. 

An interesting case that we shall not consider is where the user knows power spectra for the object and the noise and from these wants to infer p(ql9. gM). Indeed, the problem has not been solved yet, to our knowledge. 

The problem of forming p(ql9. , qM) is central to our whole approach. It is also the most difficult step. Once known and substituted into Eq. (19), a solution hm could always be at least numerically found—but not so with forming p(qu. gM). It often takes some ingenuity to frame the given prior knowledge in the form of a probability law. Some of the easier cases are taken up next. Luckily, the reader will also find them applicable in many cases. 

One scenario on which to build a p(ql9. qM) is empirical evidence, that is, actual observation of a number-count object nm prior to estimating the object. The proviso is that object nm belongs to the same class as the 

Maximum Conviction That Empirical Data Represent the Object 

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