Agree, that would foolish.

From http://andrewgelman.com/2015/03/01/precise-answers-to-the-wrong-questions/

“Statistical procedures are abstractly defined in terms of mathematics [here one would be foolish to limit mathematical approaches in this task] but are used, in conjunction with scientific models and methods, to explain observable phenomena. … When we use a statistical model to make a statistical inference [address applied problems] we implicitly assert … the theoretical world corresponds reasonably well to the real world.”

There will a lack of correspondence between the continuity of possible outcomes in the model with actual outcomes observed. (As CS Peirce put, actualities break the continuum of possibilities.)

One just needs to be aware of this disconnect and not mistakenly make a big deal out of it – one way [inconsistent MLEs will arise in applications involving just a single parameter, be wary] or an other [you should always use probabilities when calculating likelihoods]

p.s. I will have to wait until I am in the library to actually read Liu, Wu and Meeker’s paper

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