Did you try using MLE to approximate the marginal?
On Mar 3, 2013, at 5:26 AM, Ali A. Bromideh wrote: > Dear Nicole, > > First of all, my sincere gratitude goes to your kind reply. As I told to Mr. > Gunter, this is a part of my research and differs from homework. However, I > am going to clarify the problem. Suppose we have received an observation > from a Poisson distr. i.e. Y_1~Pois(Lam_1), where Lam_1~Gamma(alpha_1, > beta_1). Now, what's the empirical Bayes (EB) estimation for alpha_1 and > beta_1? > Let Y_2~Pois(Lam_2) and Lam_2~Gamma(alpha_2, beta_2). Again how can we > calculate EB for alpha_2 and beta_2? > > In fact, I read the relevant paper by Robbins at > http://www.ncbi.nlm.nih.gov/pmc/articles/PMC350425/ but it gave 0 for Y_1. > And for the Var(Y) < E(Y), it generates negative value for positive value of > alpha/beta!! > > Any idea? > > Kind regards, > > > > -----Original Message----- > From: Nicole Ford [mailto:nicole.f...@me.com] > Sent: Sunday, March 03, 2013 4:09 AM > To: Bert Gunter > Cc: Boroumideh-Ali Akbar; r-help@r-project.org > Subject: Re: [R] Empirical Bayes Estimator for Poisson-Gamma Parameters > > also, kruschke at indiana has some info on this, both online and youtube. > (if homework.) if not, more infor will be helpful. > > ~n > > > On Feb 25, 2013, at 9:41 AM, Bert Gunter wrote: > >> Homework? We don't do homework here. >> >> If not, search (e.g. via google -- "R hierarchical Bayes" -- or some > such). >> >> -- Bert >> >> On Mon, Feb 25, 2013 at 1:39 AM, Ali A. Bromideh <a.bromi...@ikco.com> > wrote: >>> Dear Sir/Madam, >>> >>> >>> >>> I apologize for any cross-posting. I got a simple question, which I > thought >>> the R list may help me to find an answer. Suppose we have Y_1, Y_2, ., > Y_n ~ >>> Poisson (Lambda_i) and Lambda_i ~Gamma(alpha_i, beta_i). Empirical Bayes >>> Estimator for hyper-parameters of the gamma distr, i.e. (alpha_t, beta_t) >>> are needed. >>> >>> >>> >>> y=c(12,5,17,14) >>> >>> n=4 >>> >>> >>> >>> What about a Hierarchal B ayes estimators? >>> >>> >>> >>> >>> >>> Any relevant work and codes in R (or S+) is highly appreciated. >>> >>> >>> >>> Kind regards, >>> >>> Ali >>> >>> >>> >>> >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> R-help@r-project.org mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >> >> >> >> -- >> >> Bert Gunter >> Genentech Nonclinical Biostatistics >> >> Internal Contact Info: >> Phone: 467-7374 >> Website: >> > http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biost > atistics/pdb-ncb-home.htm >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
