The Bayes Controversy Naive Application for Estimation---I

• Now we have derived Bayes theorem where A and B are (Borel) sets in a space populated by a random variable.

• Now a useful ``application'' of theorem is take the following choice of sets:

  A: to be Borel set given a set of experimental results---this is correct.

  B: to be a set of hypotheses, e.g., a set in space of values of a theoretical parameter---this will turn out to be flaky.

Consider an example:

• We measure scattering angles and wish to find

• when probability of observing

  is .

  Here, A is a set in space.

  B is a set in space.