Partially specified prior
  This note introduces the concept of a partially specified prior distribution for certain post hoc inference problems, where a finite population is sampled once in order to make a decision on the presence or complete absence of some attribute. If the decision is made to accept complete absence, a probability statement may be required that the population is indeed free of the attribute. A partially specified prior is shown to be advantageous in making such statements realistic and useful. 
K. Govindaraju, G. Jones