[SciPy-User] Easy Way To Find Confidence Intervals For 2D Data?

[Johann Cohen-Tanugi]

sounds like a perfect call for a scipy cookbook page!
JCT

Robert Kern wrote:
> On Tue, Jul 28, 2009 at 20:34, Joseph Smidt<josephsmidt at gmail.com> wrote:
>   
>> I have a function on a 2d grid that looks like a skewed mound. I would
>> like to calculate everything in the 68% (one sigma or standard
>> deviation) confidence interval, and 95% (two sigma) as seen done in
>> this plot: http://lambda.gsfc.nasa.gov/product/map/current/pub_papers/threeyear/parameters/images/Med/ds_f07_PPT_M.png.
>>  (The first line is 68% and second line is 95% confidence intervals.)
>>
>> I would like to the set everything in the 68% confidence interval to
>> 1, 95% to 2 and everything else to 0.  Thanks.
>>     
>
> It depends somewhat on what that function is. Is it a proper PDF?
> Let's say it is.
>
> I'll assume that the data has been normalized such that the sum of all
> the entries is 1. If not you'll have to keep track of that
> normalization constant. Let's call this array normed_pdf. What you are
> going to do is make a function that takes a value x, computes the sum
> normed_pdf[normed_pdf > x].sum(), and then subtracts the target value,
> say 0.68. Then use a root finder from scipy.optimize to find out where
> this function equals 0. Repeat for 0.95. Now just do a contour plot
> using those two values as the contour lines; e.g. in matplotlib, use
> the contour(Z, V) form.
>
>