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Hi John,
RE ESP. I’m struggling with is this Confidence intervals verses Bayesian analysis.
It seems to me that the problem is the difference between right and wrong. Confidence interval are wrong, and the Bayesian analysis is right.
But it always seems to be treated as a matter of opinion. How can this be? It’s mathematics after all….there really is a right answer.
Cheers
Mat
Mat: It’s not mathematics, it’s statistics. Or said another way, it’s an empirical question: which approach will more often lead to a correct conclusion in the real world? That’s why the debate goes on. Once you agree on what you should calculate, then it’s mathematics and there’s no debate.
I do believe the Bayesian approach to hypothesis testing will more often lead to correct conclusions. See this article by Jack Lee. I think he makes a good argument that the Bayesian approach does (or at least sometimes can do) a better job at quantifying the amount of evidence in support of a hypothesis.
By the way, there was an error in one of the examples when the article was first posted. The author has submitted a correction to the journal, but that correction may not have been posted by the time you read the article. But the essence of the argument remains valid despite the error.