[SciPy-user] KDE question

Zachary Pincus zpincus@stanford....
Fri Nov 9 15:26:15 CST 2007


Thanks a lot, Robert -- I appreciate your time and suggestions!

Zach

On Nov 9, 2007, at 3:13 PM, Robert Kern wrote:

> Zachary Pincus wrote:
>> Hello all,
>>
>> I'm using scipy.stats.gaussian_kde to estimate the a probability
>> density based on some scattered 2D samples. What I would like to do
>> eventually is plot a line that surrounds (say) 90% of the probability
>> density.
>>
>> Clearly this line corresponds to some contour of the density function
>> (which I can extract out easily enough from KDE density estimates on
>> a grid), but I'm not sure how to figure out what exact contour value
>> it is that I want.
>>
>> Given the KDE density estimates on a grid, I could empirically figure
>> out which value is closest, but I was wondering if there's a simpler
>> closed-form solution... (And apologies if it's somehow obvious; I'm
>> feeling a bit foggy-headed about this.)
>
> I don't think there is a closed-form solution for n>1-D. It  
> shouldn't be too
> hard to evaluate the KDE on a grid, then search for the value  
> between 0 and the
> peak where the integral is around 90%.
>
>
> from scipy import stats
> from scipy.optimize import brentq
>
> k = stats.gaussian_kde(data)
> xy = ... # the grid
> dxdy = ... # the area represented by each grid point
> z = k(xy)
> peak = z.max()
>
> # You can't quite do this since the function is discontinuous, and  
> never
> # actually equals 0, but you can do a search along these lines.
> # Exercise left for the reader.
> def f(s):
>     mask = z > s
>     return 0.9 - (z[mask].sum() * dxdy)
>
> brentq(f, 0, peak)
>
> -- 
> Robert Kern
>
> "I have come to believe that the whole world is an enigma, a  
> harmless enigma
>  that is made terrible by our own mad attempt to interpret it as  
> though it had
>  an underlying truth."
>   -- Umberto Eco
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