tag:blogger.com,1999:blog-10448119.post5759798876200052609..comments2024-03-23T06:42:53.608-04:00Comments on Hogg's Research: marginalized likelihoodHogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-10448119.post-58408991523510755042010-05-28T00:52:31.513-04:002010-05-28T00:52:31.513-04:00Actually, even if you make the likelihood dimensio...Actually, even if you make the likelihood dimensionless, there are nonetheless dimensional (units) reasons that you can't integrate it without first multiplying by the prior. But I am not claiming that this is in conflict with the sum rule; I am just giving another justification for the sum rule.Hogghttps://www.blogger.com/profile/18398397408280534592noreply@blogger.comtag:blogger.com,1999:blog-10448119.post-84199229732931056372010-05-26T17:58:37.647-04:002010-05-26T17:58:37.647-04:00"The likelihood is the probability of the dat..."The likelihood is the probability of the data given the model, and therefore has units of inverse data"<br /><br />The likelihood is dimensionless if you define it as the probability rather than the probability density. i.e. multiply it by dD and it's magically dimensionless!<br /><br />The real reason you need a prior to marginalise is that that's what the sum rule tells you to do. It has nothing to do with units.Brendon J. Brewerhttp://www.physics.ucsb.edu/~brewer/noreply@blogger.comtag:blogger.com,1999:blog-10448119.post-35029149824218309342010-05-26T02:05:18.500-04:002010-05-26T02:05:18.500-04:00Haha! I was doing exactly the same thing today (al...Haha! I was doing exactly the same thing today (although not with exoplanets). I declared: death to stacking analyses! and introduced several nuisance parameters per galaxy before promptly marginalising them all away. And so now I get to infer the scatter in the relations as well as the mean slopes and normalisations :-)Philhttps://www.blogger.com/profile/06436782792808539424noreply@blogger.com