Abstract
BIRNBAUM1,2 has retracted his former support3 for the likelihood approach to scientific inference4 after considering an example in which the approach would, it seems, always lead to the wrong conclusion. The import of this example2 is that there exists a hypothesis of higher likelihood than any statistical hypothesis one cares to contemplate, namely the determinist hypothesis which asserts that what was observed happened because there was no alternative, and hence has a likelihood of 1. Indeed, if the sample space is supposed continuous, this hypothesis has an infinite likelihood ratio in its favour.
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References
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Edwards, A. W. F., Nature, 222, 1233 (1969).
Ramsey, F. P., The Foundations of Mathematics and other Logical Essays (Routledge and Kegan Paul, London, 1931).
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EDWARDS, A. Likelihood. Nature 227, 92 (1970). https://doi.org/10.1038/227092a0
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DOI: https://doi.org/10.1038/227092a0
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