  Observational entropy is interpreted as the uncertainty an observer making
measurements associates with a system. So far, properties that make such an
interpretation possible rely on the assumption of ideal projective
measurements. We show that the same properties hold even when considering
generalized measurements. Thus, the interpretation still holds: Observational
entropy is a well-defined quantifier determining how influential a given series
of measurements is in information extraction. This generalized framework allows
for the study of the performance of indirect measurement schemes, which are
those using a probe. Using this framework, we first analyze the limitations of
a finite-dimensional probe. Then we study several scenarios of the von Neumann
measurement scheme, in which the probe is a classical particle characterized by
its position. Finally, we discuss observational entropy as a tool for quantum
state inference. Further developed, this framework could find applications in
quantum information processing. For example, it could help in determining the
best read-out procedures from quantum memories and to provide adaptive
measurement strategies alternative to quantum state tomography.
