If so, how do you decide the standard deviation of the noise?
It is measured experimentally obviously, the data points are meaningless without that. I have even done large sets (100+ trials) to confirm that the noise is fact gaussian which you would expect of course.
What is "the correlation matrix"?
The matrix which contains the correlation coefficients for the parameters it is essential to calculate and evaluate this for many reasons, you can not just look at the parameter uncertainties.
What data are you doing the correlation with, and what statistical techniques do you use for the correlation?
Nonlinear least-squares, Levenberg Marquet with switches for robust fitting (scaling by deviations). I keep meaning to switch to median based fitting. I have been looking lately at neural networks as well.
Of course, if you don't want to share your source code, I'll understand.
That isn't it, i'd just like to be there when you open it because your reaction would be priceless. It is actually a series of files, one is a DOS BAT file, the other a GNU scripting file and the other an awk script. There are also two input files to contain the directions/switches for the scripts and raw data. None of it is documented and the variables all look like x1yyz or similar. There is about about 10x more code than necessary as everything which was ever used is in the same file just commented out. It also isn't coherent, because I don't always run the monte carlo part, I only do that last generally once I have stabilized the fits. However the actual implementation of the algorithm is irrelevant, it is just an intersection and you can do that by however you want.
I don't think you ever explained the curve you're doing this on, but I think I figured it out.
The general procedure is just an intersect algorithm which procedes by brute force methods. The axis are just chosen to get the desired cut ratios. Sharpness vs amount of media cut for example was the one I was specifically referencing in the above. But you could use the same method on amount of media vs strokes, the meaning of the ratios would then just be different of course, so just present them accordingly.
The point isn't the particular algorithm it is that the cut ratio is a FUNCTION which is nonlinear, it isn't a constant. Once you accept this fact then you realize that you have to be careful what you say in regards to edge retention because the point at which you sharpen (how blunt the knife will get) will greatly influence the cut ratio. Then on top of this it will be effected by geometry, grit, type of cutting, etc. .
If you really want to argue an unbiased comparison then you would define the exact conditions for the conclusions to be valid or else, by definition, the results are indeed biased as I noted previously.
Is it the average x1 and x2?
You can use a linear interpolation, so it would be
y=y1+(y2-y1)/(x2-x1)*(x-x1)
This will give an average [(y2+y1)/2] when x is directly inbetween x1 and x2.
It's my observation that different steels have different ultimate sharpness limits.
Yes, but this isn't a huge difference (when proper methods are used), it is usually at the limit of the ability to resolve unless you are at very fine angles, <10 per side. If you are interested I can send you the ANOVA data I referenced which was produced by someone by a professional sharpener and the results verified under magnification as well as direct measurement for a wide variety of steels. He has also noted the influence of abrasive media and method and how using the same sharpening for all doesn't work because it can bias the results and yes even to the extent of edge retention significantly. In fact you would expect an India abrasive to bias the results in favor of the friction forged D2 over high vanadium steels for obvious reasons that the vanadium carbide is not well cut by aluminum oxide.
The hitch is that nobody knows the best possible performance of either steel A or steel B.
This is an exaggeration which is a bit pointless. The same is true for anything in an absolute sense. Ask someone who is well respected for the heat treatment/geometry and then use that and thus have a defined comparison. For example Phil Wilson has been using S90V for years so it would be very useful to compare against his blades as reference points vs some unknown sample especially if you use the geometry and edge finish that he has found optimal for the steel.
If you are interested in sharpness and the other issue I noted which is the influence of angle on edge retention :
http://www.cutleryscience.com/articles/sharpness_review.html
http://www.cutleryscience.com/articles/edge_stability_review.html
I have been planning to write the edge retention part of that for over a year detailing the various methods used and where the interpretation has to be very carefully performed and where it is misused and gives biased information and where the methods are in fact useless as they produce absurd results as I gave two examples of previously. This conclusion is not knew, in Germany it was known that you can NOT use CATRA results to infer human edge retention. It is again just physics and math not opinion. This is in fact a conclusion over 50 years old, see the work of Klemm and Kligelhoeffer.
What only astonishes me is that blades with same geometry (plus you added roughly same REST sharpness value), have so different "amount of material cut" on their first stroke, where edge retention shouldn't (probably) show yet.
They don't, like I said, the first point is actually after 20 cuts so edge retention is obviously a strong factor. It is also very possible to have a high push cutting sharpness and a low slicing aggression. I showed this years ago by showing the result of different grits/stropping on blades.
-Cliff
