35 - Normal prior and likelihood - posterior predictive distribution

This video provides a derivation of the normal posterior predictive distribution for the case of a normal prior distribution and likelihood.
If you are interested in seeing more of the material, arranged into a playlist, please visit: • Bayesian statistics: a... For more information on econometrics and Bayesian statistics, see: ben-lambert.com/

[@gonzalopolo2612]

In my opinion the "trick" is not well explained or at least for me it is not obvious at all. Why the X' distribution has to be normal? And why in the X' = (X' - theta) + theta the video considers theta first as a constant (in the X' - theta) so the resulting Normal is N(0, tehta_x) no taking into account the variance of theta, and then the theta is considered as a normalrandom variable. I know the result is correct but the path to get there for me is a little bit confusing and not justified.

[@RealMcDudu]

Note that you could do this trick thanks to convolutions. You can see my derivation here: stats.stackexchange.com/a/455073/117705

[@lizzywong1644]

thank you so much for the shortcut. Really helpful!

[@juanjosesuarez7374]

I was trying to solve the integral lmao
Thanks for this trick!

[@ccuuttww]

wow how this theta tricks works