Fits with Error Bars Outside Constaints


Can someone help me understand why coefficients in Global Fit can be returned with values inside the constraints, but with error bars far outside the constraints (by ~8 orders of magnitude). The fits visually are very good, but I'm trying to understand how to reduce these error bars and/or how much to trust these results.
The uncertainties reported for the fit coefficients is based strictly on the curvature of the chi-square surface at the solution point. It does not know about constraints. In fact, I don't know how you would take constraints into account properly when computing uncertainty, as it is a highly non-linear operation. Probably only some Monte Carlo method, like the bootstrap, would do it properly.

Very large error bars usually are a sign of "identifiability" problems, which is statistics-speak saying that your data don't constrain the model well. You can diagnose identifiability problems by generating the correlation matrix for the fit by following the instruction in DisplayHelpTopic "Correlation Matrix". You will also need to read DisplayHelpTopic "Covariance Matrix". If any off-diagonal values in the correlation matrix are close to 1 or -1 you have a problem. My rule of thumb is that "close" usually means 0.99 or more, or -0.99 or less.

John Weeks
WaveMetrics, Inc.