tag:blogger.com,1999:blog-8666091.post7686370717501464247..comments2021-05-03T21:54:48.969+02:00Comments on The Reference Frame: Should different disciplines require different confidence levels?Luboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8666091.post-16197391141421439692011-10-15T07:48:23.773+02:002011-10-15T07:48:23.773+02:00Dear Harlow, there's of course no precise quan...Dear Harlow, there's of course no precise quantification of priors but they can be estimated approximately.<br /><br />At the beginning, the priors for all "qualitatively different hypotheses" must be chosen to be comparable. Each of the mutually exclusive ones should have the probability of 1/N.<br /><br />As the evidence is accumulating, these probabilities are being adjusted, some of them are getting extremely close to 0 and others are getting very close to 1. Depending on what evidence one takes into account, one gets different numbers but sensible scientists should at least roughly agree about which priors are very high and which of them are low.<br /><br />At any rate, priors are not fixed, they're evolving as the evidence is accumulating and changing. So priors are not terribly accurate; but they're not really mysterious. The prior probability is just the posterior probability after the moment when you took your last evidence and performed the last Bayesian inference (before the new one that is awaiting you now).<br /><br />As the amount of accumulated knowledge and evidence grows, the importance of the "really initial" priors at the beginning drops.<br /><br />I think that the prior probability that Einstein is wrong before OPERA was so small that 6-sigma evidence isn't enough. More precisely, there's really a big evidence - previous evidence for relativity - that OPERA did some big mistake in their calculation of the mean value or the systematic error.<br /><br />Cheers<br />LMLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-91180947208939914792011-10-15T04:13:22.742+02:002011-10-15T04:13:22.742+02:00I'm a Bayesian. What are the priors for exper...I'm a Bayesian. What are the priors for experimental error? What was the prior that Einstein was wrong?Harlowhttps://www.blogger.com/profile/03266830002279909017noreply@blogger.com