# specifying prior distribution for parameter when no prior information alvailable

I am in the middle of finishing my undergraduate thesis which titled "Model Selection Analysis with Bayesian Model Averaging on Logistic Regression". There are some questions that I want to ask you about this BMA topics. And I will really appreciate it if you want to answer my questions. Here is the questions:

Can you give me any reference that explain the derivation of BIC approximation that based on bic.glm package? I have read reference about approximation of marginal likelihood and it can be approximated with exp(1/2 BIC), because of the BIC formula doesn't contain any information about prior distribution of parameter, then do we still need the specification of prior parameter or not? and is the bic.glm package use this marginal likelihood approximation too for computing the posterior probability of model?

The problems that i face right now is i want to analyze medical data about low-birth weight born babies, but i don't have any prior information or prior beliefs about the data. so i am not sure which prior distribution should i use for the model parameters. is using noninformative prior appropriate for the BMA analysis? or is there any suggestion which prior that seems reasonable for my case? if i have to used non-informative prior then is it okay to give the prior parameter by 0,5 for all parameter like what has been given in the default of statistical package? thank you for your kind of help. i do really appreciate it

That is the questions that I hope you to answer. Thank you for your attention for reading this, and I will really appreciate it if you answer the questions.

• The first two questions appear to relate to programming, operation or implementation issues with a package. This is off topic (see the part about Programming). Your third question is definitely on-topic but I am not sure if you have correctly stated the issue. BIC is an asymptotic approximation to minus twice the log of a posterior probability under a particular set of assumptions, including in relation to the prior. see Wikipedia here where it's stated explicitly. – Glen_b May 8 '17 at 22:44
• Please consult the first link above in order to edit your questions (it's possible to ask some kinds of programming-related questions as noted at the link -- ones that require statistical expertise but otherwise they may be better asked elsehwere), and then consider the phrasing of your third question. (If you prefer you could simply ask about the premise you hold in relation to the prior.) – Glen_b May 8 '17 at 22:45
• The use of Wikipedia as a reference doesn't prove much of course; I'll try to find you a reference that explains the situation. One prior that corresponds to BIC is mentioned here. That's not the prior I mean, though; there's yet another one that's asymptotically the same as BIC. (By contrast, this post suggests there's no prior and BIC is just log of a Bayes factor) – Glen_b May 8 '17 at 22:58
• @Glen_b Thank you for your advice, i am sorry for this incovenience. because it's my first time posting in this website. I will reask the first two question in the right forums. And i have edited my questions, i will really appreciate it if you want to answer my new question which given above. thank you very much – Muthmainah May 11 '17 at 2:17
• I've reopened it. You may get further requests to clarify parts of your question – Glen_b May 11 '17 at 2:20