Empirical Bayes Estimator for Poisson-Gamma Parameters

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.ford at me.com] 
Sent: Sunday, March 03, 2013 4:09 AM
To: Bert Gunter
Cc: Boroumideh-Ali Akbar; r-help at 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.BROMIDEH at 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




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