{"action":"created","issue":{"url":"https://api.github.com/repos/aimalz/prob-z/issues/37","labels_url":"https://api.github.com/repos/aimalz/prob-z/issues/37/labels{/name}","comments_url":"https://api.github.com/repos/aimalz/prob-z/issues/37/comments","events_url":"https://api.github.com/repos/aimalz/prob-z/issues/37/events","html_url":"https://github.com/aimalz/prob-z/issues/37","id":120488511,"number":37,"title":"try two or three different interim priors","user":{"login":"davidwhogg","id":710750,"avatar_url":"https://avatars.githubusercontent.com/u/710750?v=3","gravatar_id":"","url":"https://api.github.com/users/davidwhogg","html_url":"https://github.com/davidwhogg","followers_url":"https://api.github.com/users/davidwhogg/followers","following_url":"https://api.github.com/users/davidwhogg/following{/other_user}","gists_url":"https://api.github.com/users/davidwhogg/gists{/gist_id}","starred_url":"https://api.github.com/users/davidwhogg/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/davidwhogg/subscriptions","organizations_url":"https://api.github.com/users/davidwhogg/orgs","repos_url":"https://api.github.com/users/davidwhogg/repos","events_url":"https://api.github.com/users/davidwhogg/events{/privacy}","received_events_url":"https://api.github.com/users/davidwhogg/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"milestone":null,"comments":4,"created_at":"2015-12-04T21:21:30Z","updated_at":"2015-12-09T01:31:40Z","closed_at":null,"body":"Show that we get the right answer for the maximum marginalized likelihood, no matter what interim prior we use.  That is, choose three (say) interim priors:  One flat, one that slopes so that it prefers low redshifts, one curved (so it prefers, say, low and high over middle).  Show that the p(z) data (zPDFs) change sensibly as you change the interim prior, but that the final maximum marginalized likelihood doesn't change.\r\n\r\nThis is critical, because we are going to have *real* situations with strange interim priors (think crazy training sets...)."},"comment":{"url":"https://api.github.com/repos/aimalz/prob-z/issues/comments/163077982","html_url":"https://github.com/aimalz/prob-z/issues/37#issuecomment-163077982","issue_url":"https://api.github.com/repos/aimalz/prob-z/issues/37","id":163077982,"user":{"login":"aimalz","id":8606810,"avatar_url":"https://avatars.githubusercontent.com/u/8606810?v=3","gravatar_id":"","url":"https://api.github.com/users/aimalz","html_url":"https://github.com/aimalz","followers_url":"https://api.github.com/users/aimalz/followers","following_url":"https://api.github.com/users/aimalz/following{/other_user}","gists_url":"https://api.github.com/users/aimalz/gists{/gist_id}","starred_url":"https://api.github.com/users/aimalz/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/aimalz/subscriptions","organizations_url":"https://api.github.com/users/aimalz/orgs","repos_url":"https://api.github.com/users/aimalz/repos","events_url":"https://api.github.com/users/aimalz/events{/privacy}","received_events_url":"https://api.github.com/users/aimalz/received_events","type":"User","site_admin":false},"created_at":"2015-12-09T01:31:40Z","updated_at":"2015-12-09T01:31:40Z","body":"Yes, the dotted line (MLE) approaches the thicker line (true N(z)) with a larger survey size.  The MLE marginalizes out the individual redshift posteriors here.\r\nFlat interim prior:\r\n![truenz](https://cloud.githubusercontent.com/assets/8606810/11673893/37231602-9dea-11e5-8f1b-19e438a8979f.png)\r\nLow-z favoring interim prior:\r\n![truenz](https://cloud.githubusercontent.com/assets/8606810/11673911/5427588a-9dea-11e5-9a6c-2abef29f71bc.png)\r\nMid-z disfavoring interim prior:\r\n![truenz](https://cloud.githubusercontent.com/assets/8606810/11673927/682ef5fe-9dea-11e5-87b7-05a3ffa5e3e4.png)"}}