Revisit to the Likelihood Principle

Abstract

Undoubtedly, whether to accept the likelihood principle or not has been, and still is, one of the most crucial issues for philosophical debates on statistics, though interests in it are waning from statistical debates due to general preferences for more practical issues of statistics. The principle says all you need in parameter analyses of a statistical model is found in likelihood for the data obtained. Bayesians and likelihoodists have traditionally regarded this principle as fundamental, declining any forms of statistics which violate it. Frequentism, on the other hand, try to reject this principle, upholding error probability as a more crucial factor for statistical analyses. But arguments made so far on the likelihood principle still seem to stay on those as to what principle we prefer to choose in statistical analyses. The validity of this principle seems to have never been explored fully enough through the arguments on either side. In this paper, I briefly review how these arguments have been made and show some difficulty in maintaining the principle. I think this has some impact upon statistical practices as well.