What I was trying to emphasise is that, pace “potato”, the frequentist/Bayesian dispute isn’t just an argument about words but actually has ramifications for how one is likely to approach statistical inference—so it shouldn’t be compared to the definitional dispute “If a tree falls in a forest and no one hears it, does it make a sound?”
If someone treated frequentist approaches as though they were equivalent to Bayesian methods in general, then he would occasionally be drastically in error. PT:TLoS offers many examples of this (for example the comparison of a Bayesian “psi test” and the chi-squared test on page 300). My comment about the Gaussian distribution had in mind Jaynes’s discussion of “pre-data and post-data considerations” starting on page 499, in which he discusses the fact that orthodox practice answers the wrong question: it gives correct answers to “if the hypothesis being tested is in fact true, what is the probability that we shall get data indicating that it is true?” when the real problems of scientific inference are concerned with the question “what is the probability conditional on the data that the hypothesis is true?”, and this problem is the result of frequentist philosophy’s failure to admit the existence of prior and posterior probabilities for a fixed parameter or an hypothesis. He suggests that this conflation goes somewhat unnoticed because in the case of the commonly encountered Gaussian sampling distribution the difference is relatively unimportant, but compares another case (Cauchy sampling distributions) in which the Bayesian analysis is far superior.
On the other hand the interlocutors in the standard definitional dispute have no substantive disagreement, i.e. they actually anticipate the same things, so their disagreement amounts to nothing apart from the fact that they waste their time arguing about words.
I’ll defer to your opinion (which is probably much better informed than mine) on whether frequentist methods work well when their limitations are borne in mind.
Thanks for the clarification.
What I was trying to emphasise is that, pace “potato”, the frequentist/Bayesian dispute isn’t just an argument about words but actually has ramifications for how one is likely to approach statistical inference—so it shouldn’t be compared to the definitional dispute “If a tree falls in a forest and no one hears it, does it make a sound?”
If someone treated frequentist approaches as though they were equivalent to Bayesian methods in general, then he would occasionally be drastically in error. PT:TLoS offers many examples of this (for example the comparison of a Bayesian “psi test” and the chi-squared test on page 300). My comment about the Gaussian distribution had in mind Jaynes’s discussion of “pre-data and post-data considerations” starting on page 499, in which he discusses the fact that orthodox practice answers the wrong question: it gives correct answers to “if the hypothesis being tested is in fact true, what is the probability that we shall get data indicating that it is true?” when the real problems of scientific inference are concerned with the question “what is the probability conditional on the data that the hypothesis is true?”, and this problem is the result of frequentist philosophy’s failure to admit the existence of prior and posterior probabilities for a fixed parameter or an hypothesis. He suggests that this conflation goes somewhat unnoticed because in the case of the commonly encountered Gaussian sampling distribution the difference is relatively unimportant, but compares another case (Cauchy sampling distributions) in which the Bayesian analysis is far superior.
On the other hand the interlocutors in the standard definitional dispute have no substantive disagreement, i.e. they actually anticipate the same things, so their disagreement amounts to nothing apart from the fact that they waste their time arguing about words.
I’ll defer to your opinion (which is probably much better informed than mine) on whether frequentist methods work well when their limitations are borne in mind.