The Sense in Which Frequentist Methods Violate the Likelihood Principle
It is widely accepted that frequentist methods violate the Likelihood Principle. After all, there can be two pieces of data A and B such that the Likelihood Principle implies that A and B are evidentially equivalent with respect to the set of hypotheses H, yet frequentist methods will yield different conclusions about H depending on whether A or B is fed into them.
But What About Using Frequentist Considerations to Choose Among Priors?
There is another sense in which many frequentist methods do not violate the Likelihood Principle. A frequentist method is often equivalent (in a sense) to a Bayesian method with a particular prior probability distribution. From a Bayesian perspective, such frequentist methods involve updating a prior probability distribution in a way that does conform to the Likelihood Principle. They violate the Likelihood Principle only by using “implied priors” that vary with the sampling distribution of the experiment to be performed. [Read more…]