I was confused by this post for some time, and I feel I have an analagous but clearer example: Suppose scientist A says “I believe in proposition A, and will test it at the 95% confidence level”, and scientist B says “I believe in proposition B, and will test it at the 99% confidence level”. They go away and do their tests, and each comes back from their experiment with a p-value of 0.03. Do we now believe proposition A more or less than proposition B? The traditional scientific method, with its emphasis on testability, prefers A to B; for a bayesian it’s clear that we have the same amount of evidence for each.
Have I fairly characterised both sides? Does this capture the same paradox as the original example, and is it any clearer?
I was confused by this post for some time, and I feel I have an analagous but clearer example: Suppose scientist A says “I believe in proposition A, and will test it at the 95% confidence level”, and scientist B says “I believe in proposition B, and will test it at the 99% confidence level”. They go away and do their tests, and each comes back from their experiment with a p-value of 0.03. Do we now believe proposition A more or less than proposition B? The traditional scientific method, with its emphasis on testability, prefers A to B; for a bayesian it’s clear that we have the same amount of evidence for each.
Have I fairly characterised both sides? Does this capture the same paradox as the original example, and is it any clearer?