"If the model is correctly specified" Indeed. I had a similar realization when I observed that the estimated parameter error on a chi-square fit does not depen

"If the model is correctly specified" Indeed. I had a similar realization when I observed that the estimated parameter error on a chi-square fit does not depend on the actual chi-square value itself. This seemed preposterous to me, shouldn't the parameters be more uncertain if the fit is bad? Then I came across this passage in Numerical Recipies that said something like "remember that all of this is under the assumption that the model being fit to is actually the one from which the data points are drawn. If the reduced chi-square value is >>1, then that indicates that this is not the case and then the entire procedure is suspect."