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Sep 29, 2017 at 13:48 history edited jbowman CC BY-SA 3.0
Notational clarity
Sep 29, 2017 at 13:44 comment added jbowman Sorry about the notational differences; $;$ means essentially the same thing as $|$ in the context and I'm just more used to it. And you're right about leaving out $X$, I shouldn't have and I'll edit the answer for completeness. Your summary is correct; for finding the distribution of new observations, including predicting them, the ppd is used, but for the parameters, the posterior is used.
Sep 29, 2017 at 11:21 history bounty ended tomka
Sep 29, 2017 at 11:21 vote accept tomka
Sep 29, 2017 at 11:21 comment added tomka Thanks for your answer. Your notation $p(y_{new}:X_{new},y)$ deviates a bit from mine; shouldn\t it be conditional? Also you do not condition on $X$ here anymore. Other than this it is clear. So to summarize: for predicting conditional parameters of the regression the posterior distribution is used (the same would hold for other models e.g. linear regression), for predicting new observations the ppd is used, correct?
Sep 28, 2017 at 19:34 history edited jbowman CC BY-SA 3.0
Slight clarification of the process for calculation of $\theta$.
Sep 23, 2017 at 2:21 history edited jbowman CC BY-SA 3.0
added 8 characters in body
Sep 23, 2017 at 0:53 history answered jbowman CC BY-SA 3.0