Bayesian Statistics question

[bryce09]

I have this problem that i am doing, but i am having a major blank of how to move forward with this question. As it is I have calculated this joint probability table where n=5: (i wasn't sure how to create a table here so i did the best i could)

[π]__ [Prior] [Y=0]__ [Y=1]__ [Y=2]___ [Y=3]__ [Y=4]___ [Y=5]__ [Posterior]
[0.30] [0.1] [0.0168] [0.0360] [0.0309] [0.0132] [0.0028] [0.0002] [0.1131]
[0.45] [0.2] [0.0100] [0.0412] [0.0674] [0.0552] [0.0226] [0.0038] [0.2468]
[0.55] [0.3] [0.0057] [0.0339] [0.0828] [0.1011] [0.0618] [0.0150] [0.3032]
[0.60] [0.4] [0.0040] [0.0308] [0.0920] [0.1384] [0.1036] [0.0312] [0.3369]
.__________[0.0365] [0.1419] [0.2731] [0.3079] [0.1908] [0.0502]


And also this table with the calculation for the posterior probabilities given that we have observed y=2:

[π]_._ [Prior] [Likelihood] [Prior*Likelihood] [Posterior]
[0.30] [0.1]__ [0.309] ____[0.0309] _______[0.1131]
[0.45] [0.2]__ [0.337] ____[0.0674] _______[0.2468]
[0.55] [0.3]__ [0.276] ____[0.0828] _______[0.3032]
[0.60] [0.4]__ [0.230] ____[0.0920] _______[0.3369]
_______________________[0.2731]

It has then stated that- the likelihood is proportional to π^y.(1-π)^n-y where n=5 and y=2. Redo the calculations using that likelihood.


[π]___. [Prior] [Likelihood] [Prior*Likelihood] [Posterior]
[0.30]
[0.45]
[0.55]
[0.60]

Any help with how to go about this would be greatly appreciated

[GretaGarbo]

Because of the very narrow margin in the first post in this forum it is very difficult to se the correct page that bryce09 has inserted.

If the user click on the upper right button marked “Display” and changes from “Linear mode” to “Switch to hybrid mode”, then all of a sudden one can se a wider page and it is much more clear what bryce09 had inserted.

But then you need to switch back to “Linear mode” again otherwise the posts will not appear in correct order.

Bryce09 deserved a better layout. But I must confess that I still don’t understand the model. What is the last row in the first table?

Maybe someone who is more inclined to Bayesian statistics can give an answer.

I hope this is not homework. Or is it?