tag:blogger.com,1999:blog-10448119.post562737990438051965..comments2024-03-23T06:42:53.608-04:00Comments on Hogg's Research: don't coadd posteriorsHogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-10448119.post-17764213746150979602013-12-11T11:56:24.738-05:002013-12-11T11:56:24.738-05:00That's technically true, but usually astronome...That's technically true, but usually astronomers want to know the distribution from which the objects are drawn; in this case the radius distribution!Hogghttps://www.blogger.com/profile/18398397408280534592noreply@blogger.comtag:blogger.com,1999:blog-10448119.post-31195129481787368072013-12-11T01:13:44.732-05:002013-12-11T01:13:44.732-05:00Co-adding the posteriors is the right thing to do ...Co-adding the posteriors is the right thing to do under certain assumptions about your prior information and the question that is being asked! I bring this up merely to be pedantic, the hierarchical suggestion is usually a better model of actual prior beliefs.<br /><br />If X = {x1, x2, ..., xN} is a set of quantities for each of N objects and your prior for them (and their data) is independent, then define the "histogram" (I think some people call it the empirical measure) of your objects by f(x) = 1/N \sum_i \delta [x - x_i]. The posterior expectation of the empirical measure of these N objects is the equally-weighted mixture of the N posteriors.Brendon J. Brewerhttp://stat.auckland.ac.nz/~brewer/noreply@blogger.com