G. A. Vignaux and Bernard Robertson
The conventional portrayal of Bayes Theorem is that a likelihood ratio
for evidence under two hypotheses is combined with prior odds to form
posterior odds. The posterior becomes the prior to which a likelihood
ratio for the next item of evidence is applied and so forth. At each
stage the likelihood ratio becomes more complex and it is conditioned
upon more and more earlier pieces of evidence.
Objectors to Bayesian methods claim that this presentation does not
represent real thought processes and may not be possible in real world
A more attractive view of the Bayesian model involves the successive
refinement (or redefinition or subdivision) of hypotheses to
incorporate previous items of evidence. Then at each step different
hypotheses are compared. This approach is entirely consistent with the
logical approach to probability while accommodating, or at least
defusing, these objections.
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