ABSTRACT
The only possible difficulty in their use concerns whether the part of the full likelihood omitted carries useful information about the parameter of interest. It is, however, possible to introduce further forms of likelihood that do not correspond directly to the observation of random subsystems but which may have sufficient of the properties of likelihood to make use of the term likelihood sensible. The advantages of such generalizations are partly concerned with difficult problems with many nuisance parameters and partly with applications in which calculating the full likelihood in useful form is difficult. Profile likelihood and its adjustments are instances of this.
