ROC Curve Analysis

[ptengineer]

I'm trying to discern the SNR (in dB) from a set of ROC curves. I have noise and signal plus noise pdf's from which I generate a series or ROC curves and from this ROC plot I want to reformat the x (probability of false alarm) and y (probability of detection) axis so that the ROC curves themselves are plotted as linear functions. This is similar to plotting exponential functions on log-log graphs. I guess my question is how to I pass the x and y data through their respective inverse functions so that when I plot them I get linear functions? From this plot I could then by inspection find the distance from each and associate this with some measurable SNR.

 

[MacGyverS2000]

What class is this for?

Dan - Owner

http://www.Hi-TecDesigns.com

 

[ptengineer]

This is not for a course and I am fully aware of of the guidelines for posting on this forum. I have read through many posts in this forum, mainly in electronics and circuit engineering (which is where most of my experience has been), however I have recently been involved in the field communication & signal processing, specifically detection theory.

If you would like to know the origin of this problem (while its application is fairly vast) or more specifics, please feel free to pm me.

 

[2dye4]

I would think taking natural logarithms of the equations would be the first step

 

[ptengineer]

This does work for plotting exponential functions on log-log plots, the idea is basically the same except I'm working with integrals of chi squared probability density functions.

This website shows ROC plots for normal or Guassian distributions:

http://www.anaesthetist.com/mnm/stats/roc/Findex.htm

 

[2dye4]

You may not be able to find closed form functions for the inverse of integrals of chi squared distributions.

You can get SNR without that though as you have the noise PDF.

To my understanding the SNR is independent of the detection method and the ROC. The Receiver Operating Curve is mainly a function of the detection method.



It's compexicated thought maybe i got it backward.

 

[ptengineer]

I see what you're saying in regards to finding a closed form function and that may be my problem, I'm looking for something that doesn't exist.

You seem to be right again that SNR is independent of the detection method, detection threshold and ROC plot and this makes sense seeing that two different SNR ratios could essentially produce the same ROC plot given the right circumstances. I'm trying to reproduce the following graph so that I can graphically deduce the SNR difference between curves. This is still somewhat foggy but thanks for the points.

http://books.google.com/books?id=CV...+signals&source=gbs_summary_r&cad=0#PPA302,M1