tag:blogger.com,1999:blog-4522943003528921495.post5270254881990414189..comments2024-03-25T08:18:46.113+01:00Comments on Looking at data: A reply to Testing via credible setsAnonymoushttp://www.blogger.com/profile/01238303946435935100noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-4522943003528921495.post-83166785398700375462012-10-12T15:43:23.923+02:002012-10-12T15:43:23.923+02:00This comment has been removed by the author.Anonymoushttps://www.blogger.com/profile/01238303946435935100noreply@blogger.comtag:blogger.com,1999:blog-4522943003528921495.post-82626823887953183312012-10-12T09:24:44.708+02:002012-10-12T09:24:44.708+02:00This is reflected in the loss function in Theorem ...This is reflected in the loss function in Theorem 2: falsely accepting Θ_0 is associated with a (much) lower loss than is falsely accepting either of the alternatives. (There are many situations in which such a loss would be applicable.) If we accept Θ_0 then our loss is non-zero with probability 1. But sometimes it is better to accept a certain loss than to risk a higher loss.Anonymoushttps://www.blogger.com/profile/01238303946435935100noreply@blogger.comtag:blogger.com,1999:blog-4522943003528921495.post-8548459083363738622012-10-12T09:15:03.855+02:002012-10-12T09:15:03.855+02:00To my mind, that's the beauty of it all! All t...To my mind, that's the beauty of it all! All the prior mass (and hence also the posterior mass) is on {θ: θ>θ_0} and {θ: θ<θ_0}. This seems reasonable for most point-null problems, where we don't _really_ believe that θ=θ_0. The value θ_0 is not given special weight by putting a point-mass on it.<br /><br />If the evidence is non-conclusive, we're not sure whether θ>θ_0 or θ<θ_0, and so "believe in" Θ_0 for the time being. In a sense, accepting Θ_0 corresponds to a "no decision"-decision: of course θ is not exactly θ_0, but given the data at hand we can't say whether it is greater or less than θ_0. This seems to me like perhaps the only reasonable way to interpret most point-null problems.Anonymoushttps://www.blogger.com/profile/01238303946435935100noreply@blogger.comtag:blogger.com,1999:blog-4522943003528921495.post-90535504774041865742012-10-11T21:57:49.903+02:002012-10-11T21:57:49.903+02:00Just a naïve question: what happens when you accep...Just a naïve question: what happens when you accept the null hypothesis? If you keep a Bayesian perspective, you need to put a prior under the null, however this prior was not used in choosing between the null and the alternative...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4522943003528921495.post-41731575115698074762012-10-11T20:34:18.801+02:002012-10-11T20:34:18.801+02:00I know but too well how annoying spam comments can...I know but too well how annoying spam comments can be! Although I find it quite amusing that my comment was marked as being spam.Anonymoushttps://www.blogger.com/profile/01238303946435935100noreply@blogger.comtag:blogger.com,1999:blog-4522943003528921495.post-13951273762522990062012-10-11T14:35:18.127+02:002012-10-11T14:35:18.127+02:00Sorry about your lost comments Måns, I eventually ...Sorry about your lost comments Måns, I eventually found them in the spam box! Along with 296 others, which explains why I never check that box...!Anonymousnoreply@blogger.com