Hey all, I have a bunch of data that varies over many magnitudes. I was hoping to use log bins to capture the short and long term features of the data. My question is, how do I bin the data, and how do I assign appropriate errors so that I can fit the data to some theory (maybe a power law)? Cheers!
Probably the most straightforward method is to rescale the data as y=log_{10}(x), and then take equal intervals in binning the y data. Good question about the errors. I'm not absolutely sure, but I believe that the error would be ± the square root of the expected number of counts within a bin, at least when that count total is considerably greater than 1. This becomes problematic when the expected count is less than 1, for example 0.25±0.5 allows for negative counts, an unphysical result. Perhaps somebody who knows statistics better than I can provide a more accurate answer.
I have managed to find this website with MATLAB scripts relevant to my initial query, that may help people in the future who are asking the same, or a similar question: http://www-personal.umich.edu/~ladamic/courses/si614w06/matlab/index.html
Also, I have modified the scripts on the page given in my previous reply, and uploaded a MATLAB file to MATLAB Central http://www.mathworks.com/matlabcentral/fileexchange/27176-log-binning-of-data