The method of maximum likelihood provides a basis for many of the techniques
and methods discussed in this course. The reasons are:
The method has a good intuitive foundation. The underlying concept is that
the best estimate of a parameter is that giving the highest probability
that the observed set of measurements will be obtained.
The least-squares method and various approaches to combining errors or
calculating weighted averages, etc., can be derived or justified in terms
of the maximum likelihood approach.
The method is of sufficient generality that most problems are amenable
to a straightforward application of this method, even in cases where other
techniques become difficult. Inelegant but conceptually simple approaches
often provide useful results where there is no easy alternative.