spacer spacer spacer meaningless logo

Abstract: The answer is the likelihood principle.

This will review the state of the art, and say why it's so important.

Every philosopher knows the Principle of Total Evidence, usually associated with Carnap, which says that one should not ignore information.

"A principle which seems generally recognized,[footnote 10: Keynes, op. cit.[J.~M.~Keynes, \it A Treatise on Probability\/ (1921)], \p.313, refers to `Bernoulli's maxim, that in reckoning a probability, we must take into account all the information which we have'.] although not always obeyed, says that if we wish to apply such a theorem of the theory of probability to a given knowledge situation, then we have to take as evidence $e$ the \it total evidence\/ available to the person in question at the time in question, that is to say, his total knowledge of the results of his observations." \cite[p\p.138—139]Carnap:1947

"Bernoulli's maxim,[footnote 1: \it Ars Conjectandi, \p.215: `Non sufficit expendere unum alterumve argumentum, sed conquirenda sunt omnia, quae in cognitionem nostram venire possunt, atque ullo modo ad probationem rei facere videntur.'] that in reckoning a probability we must take into account all the information which we have" \cite[\p.313]Keynes:1921

—-

The likelihood principle is a version of this applicable to statistical inference. It says (roughly) that when one has a sample of data, one should take that sample fully into account when making inferences about hypotheses. And yet, because of the popularity of evaluating methods of inference on their long-run behaviour, the likelihood principle is frequently broken.

—-

  • This could emphasise the role of the LP in categorising theories of statistical inference. I don't think anyone's really made a big deal about that yet. B&W's book doesn't do that: they want to push Bayesianism. And the other books want to push the use of raw likelihoods or raw likelihood ratios.

  • where can I publish such a long paper? or should it be just a summary?

  • note to self: say something about 'the importance of protocol' in Hutchison BJPS, Dowe, Korb etc.