Читать книгу Probability and Statistical Inference - Robert Bartoszynski - Страница 23

Candidates for a certain job are characterized by their level of skills required for the job. The actual value of is not observable, though; what we observe is the candidate's score on a certain test. Thus, the sample point in is a pair , and only one coordinate of , , is observable.

The objective might be to find selection thresholds and , such that the rule: “accept all candidates whose score exceeds ” would lead to maximizing the (unobservable) number of persons accepted whose true level of skill exceeds . Naturally, to find such a solution, one needs to understand statistical relation between observable and unobservable .

Another example when the points in the sample space are only partially observable concerns studies of incidence of activities about which one may hesitate to respond truthfully, or even to respond at all. These are typically studies related to sexual habits or preferences, abortion, law and tax violation, drug use, and so on.