The probability contours in T and beta space, used in this analysis, are generated from a chi^2 calculation. The T beta space is laid out in a 2-D histogram where each cell of the histogram contains the chi^2 as described below.
The chi^2 is calculated from the difference between the real spectrum and the Siemens and Rasmussen (SR) spectrum. The equation for chi^2 is:

                                    (real_spectrum[i]-SR_spectrum[i])^2
chi^2 = SUM(i)        ----------------------------
                                                         error[i]^2

For each cell of the T beta histogram, the SR spectrum changes with the T and beta of that cell. Therefore the chi^2 is different for each cell. Plotting the 2-D histogram one can see the valley in the chi^2 space.

From tables of chi^2 probability (such as from Advanced Engineering Mathematics, Erwin Kreyszig, John Wiley & sons) one can then determine from the number of degrees of freedom and the desired probability level the corresponding chi^2. The 2-D chi^2 plot is then drawn with a contour of the chi^2 determined from the probability table.