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It is often considered surprising and controversial. In particular, if the experiment performed included "controversial" stopping criteria then you could imagin

by tel 9y ago

It is often considered surprising and controversial. In particular, if the experiment performed included "controversial" stopping criteria then you could imagine the same data arising but not trusting each result identically. Arguments exist for each side.

RA_Fisher 9y ago
Yep, I should add that portion. You're spot on. This was surprising to me because I've shown both models contain the same information but identical Frequentist hypothesis tests will show different p-values. This unshown part is what suprised me. The next post! :)
- tel 9y ago
  Your user name is absolutely lovely given this topic :)
  - RA_Fisher 9y ago
    Haha, you could say I've come full circle. :-p
contravariant 9y ago
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.

by tel 9y ago

RA_Fisher 9y ago

Yep, I should add that portion. You're spot on. This was surprising to me because I've shown both models contain the same information but identical Frequentist hypothesis tests will show different p-values. This unshown part is what suprised me. The next post! :)

tel 9y ago
Your user name is absolutely lovely given this topic :)
- RA_Fisher 9y ago
  Haha, you could say I've come full circle. :-p

contravariant 9y ago

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.