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So I guess the problem here is that to calculate the probability that the likelihood exceeds a certain bound can't be calculated solely from the likelihood (+pr

So I guess the problem here is that to calculate the probability that the likelihood exceeds a certain bound can't be calculated solely from the likelihood (+prior) itself. Yet interestingly, the likelihood + prior is enough to make statements about the distribution of the parameters you're looking at. So you can say something about the certainty that your parameter exceeds a certain bound. I suppose it really depends on your application which you'd want to use.

tel 9y ago
That's a Bayesian perspective, but the heart of the Likelihood Principle is that non-Bayesians/non-Likelihoodists can find reason to believe that the Likelihood doesn't really contain all of the relevant information for making inferences.
- nonbel 9y ago
  > "all of the relevant information for making inferences" I think this terminology is way too strong. Obviously the context matters. For example, the way the data is collected (whether or not the data collector is a known liar/p-hacker, the sensor is known to malfunction at certain temperatures, etc) should affect inference.
  - tel 9y ago
    Right, and the Likelihoodist/Bayesian would put those details into the model. Real world concerns get handled by each side in acceptable ways, but very special details about how sampling and posterior distributions differ are what make this tricky.