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Also model A may be something like "Standard Model w/o sterile neutrinos", while model B is "Standard model w/ sterile neutrinos". My understanding is these wil

Also model A may be something like "Standard Model w/o sterile neutrinos", while model B is "Standard model w/ sterile neutrinos". My understanding is these will be supported by all the same previous evidence. In that specific case, no, a number of existing experiments appeared to confirm the "w/o sterile neutrinos" model, so it was assumed that was correct. Just one older experiment fit the "w/ sterile neutrinos" model; that has only recently been reproduced successfully, so now that model is back on the table. But it's still possible that it's just a measurement error. And anyway, if you want to include prior info there is a principled method of doing so: Bayes' Rule. The method described here is indirect, obfuscated, qualitative, and open to all sorts of bias. In general it seems inferior in every which way, why has Bayes' Rule been rejected for this purpose? Good question, I don't know! I wonder if some of the LHC people commenting here can talk about the reason for sticking with Frequentist over Bayesian statistics? I suspect this gets into some pretty deep issues around the philosophy of science. Are we looking for the "correct" theory, or just successively better approximations to reality, or what? I don't think you can easily say "the Standard Model is incorrect" -- we know it's incomplete, hence incorrect, but it also fits experimental data incredibly well, so it must be a close approximation to some level of reality at the very least. (edit to clarify: what I mean is, I'm not sure how you set a prior confidence on "is the Standard Model correct?" in a Bayesian sense, since we already know it's partially correct and partially incorrect.)

nonbel 8y ago
>"In that specific case, no, a number of existing experiments appeared to confirm the "w/o sterile neutrinos" model, so it was assumed that was correct. Just one older experiment fit the "w/ sterile neutrinos" model; that has only recently been reproduced successfully, so now that model is back on the table. But it's still possible that it's just a measurement error." I was talking about all the other types of observations used to support the standard model. Afaik the existence of sterile neutrinos would not change the predictions. >"Good question, I don't know! I wonder if some of the LHC people commenting here can talk about the reason for sticking with Frequentist over Bayesian statistics?" It isn't really a matter of frequentist vs bayesian statistics. Frequentist stats looks like what you see in Figure 1 here (my venn diagram is just a simpler version of it): http://rsta.royalsocietypublishing.org/content/231/694-706/289 http://rsta.royalsocietypublishing.org/content/231/694-706/2... However, it is put forward that prior information should be involved in interpreting the results of the significance test. This idea has been rejected by all the giants and founders of modern stats (Fisher, Neyman, Pearson, etc). Its just some ad hoc thing come up with by stats 101 authors. >"I suspect this gets into some pretty deep issues around the philosophy of science. Are we looking for the "correct" theory, or just successively better approximations to reality, or what?" We're supposed to be comparing the predictions derived from our theories/models to data collected after the prediction was made and use these predictions to come up with useful tech and perform amazing feats. >"I'm not sure how you set a prior confidence on "is the Standard Model correct?" in a Bayesian sense, since we already know it's partially correct and partially incorrect.)" The current solution seems to be performing an elaborate ritual that obscures the true method of using collective opinion.

nonbel 8y ago

>"In that specific case, no, a number of existing experiments appeared to confirm the "w/o sterile neutrinos" model, so it was assumed that was correct. Just one older experiment fit the "w/ sterile neutrinos" model; that has only recently been reproduced successfully, so now that model is back on the table. But it's still possible that it's just a measurement error." I was talking about all the other types of observations used to support the standard model. Afaik the existence of sterile neutrinos would not change the predictions. >"Good question, I don't know! I wonder if some of the LHC people commenting here can talk about the reason for sticking with Frequentist over Bayesian statistics?" It isn't really a matter of frequentist vs bayesian statistics. Frequentist stats looks like what you see in Figure 1 here (my venn diagram is just a simpler version of it): http://rsta.royalsocietypublishing.org/content/231/694-706/289 http://rsta.royalsocietypublishing.org/content/231/694-706/2... However, it is put forward that prior information should be involved in interpreting the results of the significance test. This idea has been rejected by all the giants and founders of modern stats (Fisher, Neyman, Pearson, etc). Its just some ad hoc thing come up with by stats 101 authors. >"I suspect this gets into some pretty deep issues around the philosophy of science. Are we looking for the "correct" theory, or just successively better approximations to reality, or what?" We're supposed to be comparing the predictions derived from our theories/models to data collected after the prediction was made and use these predictions to come up with useful tech and perform amazing feats. >"I'm not sure how you set a prior confidence on "is the Standard Model correct?" in a Bayesian sense, since we already know it's partially correct and partially incorrect.)" The current solution seems to be performing an elaborate ritual that obscures the true method of using collective opinion.