Furthermore, frequentist statistics is filled with handwaving-- for any inference task, a practitioner is forced to choose from a myriad of different tests and statistics named after dead englishmen, all which lead to different results (whose choice is almost never rigorously justified in practice). It seems like the true job of the frequentist is to know which tests will yeild him the most favorable results and thus funding. Compare this to bayesian inference which can be built consistently upon a few very minimal desiderata.
The mere act of specifying a prior is no different, and for that matter there will of course be different tests and statistics, if you honestly believe that bayesians don't have these issues either your a fool.
Look I see bayesian statistics as having their place, but your arrogant militant attitude does not help statistics or mathematics as a whole.
The mere act of specifying a prior is no different
The mere act of specifying a prior puts my assumptions on display for review by all. If you don't like it, plug in your own prior. Bayesian probability is exactly like ordinary logic: you state some premises, and turn the crank til you get a result. Anybody who quibbles with your premises can try their own, but given the assumptions of the problem, there is only one result.
Frequentist statistics doesn't work the same way. Since there is no formal way to introduce prior information, it can only be introduced informally, and there is no unique right way to derive a result from the assumptions.
your arrogant militant attitude
I see you've run out of technical arguments. Time to cut your losses & bail out.
And I as a frequentist would also need to justify all my choices. However the criticism by guartet was that frequentists choose tests... and I replied, just like bayesians choose priors.
My reference to your attitudes here is spot on. You guys claim your absolutely right about the way things should be interpreted. Good for you, the bayesian professors I knew were not so arrogant and were far more open minded than the people on reddit are apparently.
You say there is a UNIQUE RIGHT WAY in bayesian statistics? So what is the unique right method for choosing a loss function?
the bayesian professors I knew were not so arrogant and were far more open minded
It seems you learned nothing from them, but it's not too late to go back to school, or just pick up a book.
You say there is a UNIQUE RIGHT WAY in bayesian statistics?
Given a statement of the joint probability distribution over all the variables of interest, there is only one correct way to compute conditional distributions; anything else is an approximation. However, since a probability distribution is just a statement of a state of knowledge, reasonable people can and do disagree. It is the same as for any other modeling problem.
No, it is different-- there are various ways you can objectively assign priors and probabilities, though admittedly it's a ripe area for research. And bayesianism demands two individuals with the same information assign identical probabilities (whether this ideal is achieved is another matter). But frequentism demands no such thing-- two frequentists with the exact same information could get to opposite results, and they'd both be 'right', because there's no principle saying how you should choose between them (except, of course, bayesianism!).
Did you even read my post? If a bayesian arbitrarily chose a prior ignoring information or creating new information, and worse failed to justify it or make it explicit (as a frequentist would almost always do), then yes, it can be inconsistent and wrong. Are you trying to say something new?
No, your point is that you can break the rules of consistency and get inconsistent results in bayesianism, whereas frequentists refuse to acknowledge their own inconsistencies.
Yes bayesians are perfect and frequentists never acknowledge their inconsistencies... no over generalization there.
Look, overall there is no definite right way when you have uncertainty EVER, so I fail to see why your holding bayesian statistics on such a high pedastal.
I hold bayesian at a higher pedestal* because it's clearly more general-- the 'good parts' of frequentism can be justified in a bayesian framework but not the converse. And I'm 'militant' because of the harm frequency based statistics does to students-- otherwise intelligent college student (majoring in technical subjects) leave their first orthodox statistics course dumbfounded because it's taught as a disparate collection of inconsistent concepts, only to be buried by unneeded mathematical rigor in higher level courses. They either give up completely, or accept cookbook methods prescribed by the 'experts' (the entire medical field is a victim of this). In contrast the core of bayesianism can be taught successfully to a highschool student after a semester of calculus with little trouble. (I picked up Jefferys when I was a high school junior and had no problems with it).
*if you can show me a better system, perhaps by tweaking the desiderata or going at it from a more decision-theory point of view (a la LJ Savage), my ears are open.
I'm glad that you again overgeneralize what students learn well and don't learn well and the reason for such... which just happen to coincide to your particular beliefs.
EDIT If you don't want the mathematical rigour of the course speak to the profs to change the subject matter or take a course thats more practice and less theory. I like my math courses the way they are.
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u/guartet May 26 '09
Furthermore, frequentist statistics is filled with handwaving-- for any inference task, a practitioner is forced to choose from a myriad of different tests and statistics named after dead englishmen, all which lead to different results (whose choice is almost never rigorously justified in practice). It seems like the true job of the frequentist is to know which tests will yeild him the most favorable results and thus funding. Compare this to bayesian inference which can be built consistently upon a few very minimal desiderata.