[R] Empirical Bayes Estimator for Poisson-Gamma Parameters

[Nicole Ford]

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.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]]
>>> 
>>> ______________________________________________
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>>> PLEASE do read the posting guide
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>>> 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
>> 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.
> 
>