[SciPy-User] Sampling from an arbitrary distribution.

[Neal Becker]

josef.pktd at gmail.com wrote:

> On Tue, Mar 29, 2016 at 7:10 PM, Andrew Nelson <andyfaff at gmail.com> wrote:
>> Hi all,
>> I wish to sample from an arbitrary probability density distribution. At
>> the moment I don't have a functional form for the density distribution
>> (so I'm not sure if I can subclass scipy.stats.rv_continuous)
>>
>> What I do have is an array containing (finely) histogrammed samples of
>> the distribution. I found some pre-existing code
>> (http://www.nehalemlabs.net/prototype/blog/2013/12/16/how-to-do-inverse-transformation-sampling-in-scipy-and-numpy/)
>> which I successfully modified to deal with pre-histogrammed data.
> 
> I was very successful using linear interpolation for the ppf to
> generate random samples, which corresponds to a histogram distribution
> http://jpktd.blogspot.ca/2012/12/visual-inspection-of-random-numbers.html
> 
> 
>>
>> Q1: Can I still subclass scipy.stats.rv_continuous to sample from my
>> arbitrary distribution? e.g. use the histogram to construct the object
>> and refer to this histogram when overriding _pdf.
> 
> It's very inefficient to generate random numbers if only the pdf is
> defined. The default generic approach uses ppf which needs cdf which
> needs. So you would better also define cdf and ppf.
> 
> 
>> Q2: If not, then is it worth adding functionality for this kind of
>> sampling? Where would it belong scipy.stats or numpy.random?
> 
> It might not fit well into the current scipy.distribution setup
> because that is mostly stateless. In this case it could be an
> advantage to store the interpolation arrays. Or maybe the advantage is
> not so large if creating the interpolator is cheap
> 
> A Histogram distribution would be the continuous analog to the
> arbitrary finite number of points discrete distribution, so might fit
> as well.
> 
> Josef
> 
>>
>> A.
>>
>>
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You might want to look at unuran.