Comparison of Two Error Estimates in Maximum Likelihood---I

• Note that physics books (Solmitz is an exception) don't mention method (a) of finding error in maximum likelihood method.

• On the other hand, mathematics books never mention (b) as a serious method.

• They do, however, prove (a) and (b) are the same for large n (as we indicated in example above) for general distribution.

• As far as I can see, method (a) is only correct definition of error.

  It follows that method (b) is wrong when it differs from method (a).

  (b) does differ from (a) for small n when, in particular, likelihood isn't Gaussian.

  So again warnings for small n (``plot likelihood'') are very dubious.