[SciPy-User] Unit testing of Bayesian estimator

[Bruce Southey]

On 11/09/2009 12:06 PM, Anne Archibald wrote:
> 2009/11/9 Bruce Southey<bsouthey at gmail.com>:
>
>    
>> I do not know what you are trying to do with the code as it is not my
>> area. But you are using some empirical Bayesian estimator
>> (http://en.wikipedia.org/wiki/Empirical_Bayes_method) and thus you lose
>> much of the value of Bayesian as you are only dealing with modal
>> estimates. Really you should be obtaining the distribution of
>> "Probability the signal is pulsed" not just the modal estimate.
>>      
> Um. Given a data set and a prior, I just do Bayesian hypothesis
> comparison. This gives me a single probability that the signal is
> pulsed. You seem to be imagining a probability distribution for this
> probability - but what would the independent variables be? The
> unpulsed distribution does not depend on any parameters, and I have
> integrated over all possible values for the pulsed distribution. So
> what I get should really be the probability, given the data, that the
> signal is pulsed. I'm not using an empirical Bayesian estimator; I'm
> doing the numerical integrations directly (and inefficiently).
>    
Here are two links on what I mean with reference to the binomial case:
http://lingpipe-blog.com/2009/09/11/batting-averages-bayesian-vs-mle-estimate/

TEACHING OF BAYESIAN ESTIMATION OF “P” PROBABILITY
IN A BERNOULLI PROCESS:
http://www.stat.auckland.ac.nz/~iase/publications/17/C439.pdf


I do not know your area but you should be able to do something similar.

Bruce