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From: Obaid Mushtaq on 2 Aug 2010 14:54
Hi all,

I have this simple question. If the answer is yes, please tell me if it is possible to preserve the variance of the interpolated data. You can take me as a noobie in Statistics.

Sample code follows:

xMin=0; xMax=1; yMin=0; yMax=1;

d=0.01;
x=xMin:d:xMax;
y=yMin:d:yMax;
[X,Y]=meshgrid(x,y);
[r,c]=size(X);
Z = 8*randn(r,c)+10;
mean(reshape(Z,1,prod(size(Z))))
var(reshape(Z,1,prod(size(Z))))

res=0.001;
xi=0:res:1;
yi=0:res:1;
[Xi,Yi] = meshgrid(xi,yi);
Zi = interp2(X,Y,Z,Xi,Yi);
[ri,ci]=size(Xi);
mean(reshape(Zi,1,prod(size(Zi))))
var(reshape(Zi,1,prod(size(Zi))))

I would appreciate any comments.

BR,

Obaid
From: Tom Lane on 2 Aug 2010 17:53
> I have this simple question. If the answer is yes, please tell me if it is
> possible to preserve the variance of the interpolated data. You can take
> me as a noobie in Statistics.

>> x = 1:2;
>> y = 1:2;
>> var(y)
ans =
0.5000
>> xi = [1 1.5 2];
>> yi = interp1(x,y,xi)
yi =
1.0000 1.5000 2.0000
>> var(yi)
ans =
0.2500

This one-dimensional example shows that it's certainly possible that the
interpolation results will have a lower variance than the original data. I'm
not sure what you want to do about that. You could add noise to the output
from interp1/2, but then the results will no longer interpolate the original
data. Maybe you can explain what you're trying to accomplish.

-- Tom


From: John D'Errico on 2 Aug 2010 18:16
"Obaid Mushtaq" <obaidmushtaq(a)yahoo.com> wrote in message <i37490$ic7$1(a)fred.mathworks.com>...
> Hi all,
>
> I have this simple question. If the answer is yes, please tell me if it is possible to preserve the variance of the interpolated data. You can take me as a noobie in Statistics.
>

Yes, there is NO presumption at all that an interpolation
will preserve the variance of an array. Therefore it will
do so.

I have no idea why you wish a variance preserving
interpolant, but I would suggest that no tool does
what you want. People always want things they can't
have though.

John
From: Obaid Mushtaq on 3 Aug 2010 09:10
Hi,

Thanks for your response. Actually I get random shadowing values at a pre-defined 2D grid and these values have a particular variance as they are normally distributed.

After that I want to interpolate the values over a finer grid but the variance of the interpolated version changes as I showed you in case of ML functions.

See [1] p.p 44. They say that the linear interpolation formula guarantees the same variance. I was confused why ML's function is not preserving.

BR,

Obaid

[1] http://www.ieee802.org/16/tgm/docs/80216m-08_004r5.zip

"Tom Lane" <tlaneATmathworksDOTcom(a)nospam.com> wrote in message <i37epl$skj$1(a)fred.mathworks.com>...
> > I have this simple question. If the answer is yes, please tell me if it is
> > possible to preserve the variance of the interpolated data. You can take
> > me as a noobie in Statistics.
>
> >> x = 1:2;
> >> y = 1:2;
> >> var(y)
> ans =
> 0.5000
> >> xi = [1 1.5 2];
> >> yi = interp1(x,y,xi)
> yi =
> 1.0000 1.5000 2.0000
> >> var(yi)
> ans =
> 0.2500
>
> This one-dimensional example shows that it's certainly possible that the
> interpolation results will have a lower variance than the original data. I'm
> not sure what you want to do about that. You could add noise to the output
> from interp1/2, but then the results will no longer interpolate the original
> data. Maybe you can explain what you're trying to accomplish.
>
> -- Tom
>
From: us on 3 Aug 2010 09:27
"Obaid Mushtaq" <obaidmushtaq(a)yahoo.com> wrote in message <i394fv$8kd$1(a)fred.mathworks.com>...
> Hi,
>
> Thanks for your response. Actually I get random shadowing values at a pre-defined 2D grid and these values have a particular variance as they are normally distributed.
>
> After that I want to interpolate the values over a finer grid but the variance of the interpolated version changes as I showed you in case of ML functions.
>
> See [1] p.p 44. They say that the linear interpolation formula guarantees the same variance. I was confused why ML's function is not preserving.
>
> BR,
>
> Obaid
>
> [1] http://www.ieee802.org/16/tgm/docs/80216m-08_004r5.zip

well...
carefully(!) read the pages 44 and 45, again - and carefully(!) listen to what they really say...

us
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