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 as 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 inferential problems.
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.
KeywordsLikelihood Ratio Reasonable Doubt Probability Ratio Posterior Odds Prior Odds
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