Closed surbut closed 10 years ago
stephens999
commented
10 years ago I don't think I understand the question. Can you try again? It might help to put in the latex subscripts ($B_i$ etc, and \int, \Theta) properly, and be explicit about what data are here?
surbut
commented
10 years ago Hi Matthew,
Thanks very much for your response. Can I maybe just show you quickly after class? It might make things clearer. It was comparing my notes from class with some notes I had from a computer science class with David Blei (attached, pages 3 and 4), and I just wanted to make sure I understood the hierarchical flow of parameter information in an example which dealt with a child's height given underlying family-sepcific height 'mu_i' generated by an overall population generating height parameter theta. Does the posterior on the hyperparameter which generates the family-averages of height in this case incorporate information from all heights X or only the information omitting the X_i data point? Perhaps I'm making my life more difficult by using outside notes for examples ... The Berger text is fantastic though.
Thanks very much and sorry to bother - I'm enjoying the challenging class! Sarah
On Apr 28, 2014, at 10:05 AM, stephens999 notifications@github.com wrote:
I don't think I understand the question. Can you try again? It might help to put in the latex subscripts ($B_i$ etc, and \int, \Theta) properly, and be explicit about what data are here?
— Reply to this email directly or view it on GitHub.
stephens999
commented
10 years ago sure. MS
On Mon, Apr 28, 2014 at 10:52 AM, surbut notifications@github.com wrote:
Hi Matthew,
Thanks very much for your response. Can I maybe just show you quickly after class? It might make things clearer. It was comparing my notes from class with some notes I had from a computer science class with David Blei (attached, pages 3 and 4), and I just wanted to make sure I understood the hierarchical flow of parameter information in an example which dealt with a child's height given underlying family-sepcific height 'mu_i' generated by an overall population generating height parameter theta. Does the posterior on the hyperparameter which generates the family-averages of height in this case incorporate information from all heights X or only the information omitting the X_i data point? Perhaps I'm making my life more difficult by using outside notes for examples ... The Berger text is fantastic though.
Thanks very much and sorry to bother - I'm enjoying the challenging class! Sarah
On Apr 28, 2014, at 10:05 AM, stephens999 notifications@github.com wrote:
I don't think I understand the question. Can you try again? It might help to put in the latex subscripts ($B_i$ etc, and \int, \Theta) properly, and be explicit about what data are here?
— Reply to this email directly or view it on GitHub.
— Reply to this email directly or view it on GitHubhttps://github.com/stephens999/stat302/issues/8#issuecomment-41575514 .
Hi again,
In class we showed the utility of incorporating the surrounding xi to provide information on the hyper parameter, in this case the mu and sigma2 from which the betai were generated. This might be a small point, but in the fully bayesian case with 'theta' representing the hyperparameters mu and sigma2 , where: p(Bi|data)=int(p(Bi|data,theta )p(data,theta)dtheta p(Bi|data)=int(p(xi|Bi) * p(Bi|theta) * p(theta) * int (prod(data|Bj)(Bj|theta)dBj)) dTheta
might we want do incorporate only the data excluding our data point of interest (i.e., in the inner integral which expresses pr(data,theta) integrating out the intermediate parameters Bj, consider only those data with Bj not equal to Bi? I was just thinking that this might allow the other data to provide more insight into the posterior distribution of the hyper parameter without integrating out the Bi of whom which we are interested. I apologize for notation - I am a newbie but trying vigorously to learn.