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Philosophy

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    Likelihood is irrelevant to priors and your ref is specifically 'law of likelihood' in Likelihood principle: In Bayesian statistics, this ratio is known as the Bayes factor, and Bayes' rule can be seen as the application of the law of likelihood to inference...Combining the likelihood principle with the law of likelihood yields the consequence that the parameter value which maximizes the likelihood function is the value which is most strongly supported by the evidence. This is the basis for the widely used method of maximum likelihood....
    – Double Knot
    Commented Oct 25, 2023 at 1:25
  • Priors are relevant to the Bayes factor in that the hypotheses may have nuisance parameters, and ideally it would be the ratio of marginal likelihoods, after having integrated over those nuisance parameters, weighted by their prior distributions.
    – Dikran Marsupial
    Commented Oct 25, 2023 at 17:06