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> All mathematicians and engineers have access to the whole world of theorems and algorithms and techniques, all of them true, or meeting their specifications.

> All mathematicians and engineers have access to the whole world of theorems and algorithms and techniques, all of them true, or meeting their specifications. Only crazy mathematicians would think nothing of a set of tools that contradict each other. If I recall correctly, frequentist methods often yield different (and therefore contradictory) results depending on the way you look at the data. That's crazy. I also have read your link: the prior problem can easily be solved by just communicating the likelihood ratios. Those are pretty much indisputable, and the actual contribution of the paper. Let the others start from their own priors. We have to chose one anyway.

tel 14y ago
Bayesian methods are also inconsistent wrt infinitely small changes in priors. See Wasserman's blog for more details. If you're worried about the Likelihood Principle causing "frequenting" inconsistency then you're taking a bitter pill in that not everyone actually believes the LP, the assertions leading to it can be debated, and, further, Likelihoodist methods (like most of Fisher's work) are not affected by it while still worrying themselves with coverage instead of posteriors.
- loup-vaillant 14y ago
  > Bayesian methods are also inconsistent wrt infinitely small changes in priors. See Wasserman's blog for more details. That looks like it would falsify the method instantly. Or are you talking about merely small changes in priors? Anyway, I can't find the details you speak of, do you have a link? As for the likelihood principle, my math is rusty at the moment, I'll check. I expect however that I will just accept this principle as obvious. People don't believe it? They probably had the wrong teachings, just like most religious people. I'm not sure I know on a gut level how hopelessly wrong people often are. I'm not sure I properly feel the fear that should come with the possibility that I am hopelessly wrong. But I have an idea.

tel 14y ago

Bayesian methods are also inconsistent wrt infinitely small changes in priors. See Wasserman's blog for more details. If you're worried about the Likelihood Principle causing "frequenting" inconsistency then you're taking a bitter pill in that not everyone actually believes the LP, the assertions leading to it can be debated, and, further, Likelihoodist methods (like most of Fisher's work) are not affected by it while still worrying themselves with coverage instead of posteriors.

loup-vaillant 14y ago
> Bayesian methods are also inconsistent wrt infinitely small changes in priors. See Wasserman's blog for more details. That looks like it would falsify the method instantly. Or are you talking about merely small changes in priors? Anyway, I can't find the details you speak of, do you have a link? As for the likelihood principle, my math is rusty at the moment, I'll check. I expect however that I will just accept this principle as obvious. People don't believe it? They probably had the wrong teachings, just like most religious people. I'm not sure I know on a gut level how hopelessly wrong people often are. I'm not sure I properly feel the fear that should come with the possibility that I am hopelessly wrong. But I have an idea.