How Can I Quantitatively Validate My Numerical Model Against Experimental Data?

[py_engineer]

Hi,

I developed this numerical model where I solve a set of PDEs that allows me to simulate an imaging detector with different parameters, etc.

Now, I would like to compare my model with a particular case where experimental data has been obtained. I made a very simple plot to explain what I want to do:

http://www-personal.umich.edu/~pyemelie/plot.bmp

The variable in the experimental data is 'RA' and is plotted versus temperature T.

Using my numerical model, I can simulate the detector in the conditions of the experimental case, and simulate 'RA' as well versus temperature (at the same temperature points than the experimental data, as shown in the little figure).

If I plot the experimental 'RA' and my simulated 'RA' versus T on the same graph, that should give something similar to what you can see in the image.

Now, I would like to find some theoretical parameters, correlation parameters or something like that (I am not really good with Statistics..) in order to give a quantitative value of how close my simulation data set is from the experimental one. Could anyone give me some advice/recommendations on this??

I don't want to go too deep in the model validation. I think that just a graphical analysis (such as just plotting the simulated and experimental data on the same graph) and a quantitative parameter would do.. But I would like still to use some kind of parameter with a theoretical background (meaning, I don't just want to make up my own parameter).

I want to point out that (in case it's relevant), as you see in the plot, the 'RA' versus T is not a linear plot, and that the 'RA' data points can vary by several orders of magnitude.

Thanks a lot!

 

[Predictor]

It's not clear to me whether you are more interested in RA or log(RA), but I don't see why a simple mean absolute error or mean absolute percentage error couldn't be used to characterize your model's error, though it should be calculated on observations not used to fit the model function.


-Will Dwinnell
http://matlabdatamining.blogspot.com/"