[R] Empirical Bayes Estimator for Poisson-Gamma Parameters

[Ali A. Bromideh]

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
>> 
>> 
>> 
>> 
>>        [[alternative HTML version deleted]]
>> 
>> ______________________________________________
>> R-help at 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 at r-project.org mailing list
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> PLEASE do read the posting guide
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> and provide commented, minimal, self-contained, reproducible code.