Misconception: The Relative Belief Ratio Equals the Marginal Likelihood

The Misconception The relative belief ratio (e.g., Evans 2015, Horwich 1982/2016) equals the marginal likelihood. The Correction The relative belief ratio is proportional to the marginal likelihood. Dividing two marginal likelihoods (i.e., computing a Bayes factor) cancels the constant of proportionality, such that the Bayes factor equals the ratio of two complementary relative belief ratios (Evans 2015, p.109, proposition 4.3.1).…
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