Introducing uncertainty to histogram bins

Hi everyone,

I'm currently constructing a graph where some y values are binned to specific intervals of x-values. My issue here is that due to experimental limitations the bin-edges I define should have a fixed integer value uncertainty (e.g. +- 25) so that the y values that fall into these uncertainties are also counted. The codes I'm using for defining the bins are as the following:

Interval = 1000000;
NumberOfPoints = max(x)/Interval;
binEdge = linspace(min(x),max(x),NumberOfPoints);
[N,Edges] = histc(x,binEdge);
Intensity = accumarray(Edges,y');

So the question is how can I modify this in such a way to introduce the uncertainties to the edges of the bins?

Your help is greatly appreciated

[Guillaume]

So to clarify, you want a value within ± 25 of a bin edge to be counted in both bins, or something else?

[Darui Li]

Yes that is correct :)

Answer 1

[Guillaume]

Assuming that the spacing between your bins is greater than your uncertainty, I would simply create additional bins around each edge:

   binEdge = 0:100:1000; %for example
   uncertainty = 25;     %for example
   assert(all(diff(binEdge) > uncertainty), 'bins won''t be monotinically increasing')  

   newbinEdges = [binEdge - uncertainty; binEdge; binEdge + uncertainty];
   newbinEdges = newbinEdges(:)

   [~, idx] = histc(x, newbinEdges);  %note that the 2nd return value of histc are not edges but indices
   Intensity = accumarray(idx, y');

   %Now add the uncertainty bins to central bins:
   %The central bins (original bins) are at indices 2:3:end
   %Indices 1:3:end are values within -uncertainty of the bin edges
   %Indices 3:3:end are values within +uncertainty of the bin edges
   Intensity = Intensity(2:3:end) + Intensity(1:3:end) + Intensity(3:3:end)