CONFIDENCE BAND APPROXIMATION USING INTERVAL ARITHMETIC

Simon BROWN, Kevin C. PEDLEY, Noorzaid MUHAMAD, David C. SIMCOCK

 Abstract. Confidence bands are commonly obtained from linear regression, but they are rarely shown for nonlinear functions. In part this is due to mathematical complexity. A simple, intuitive and easily automated alternative is to employ interval arithmetic to approximate the confidence band. We illustrate the method by applying it to a straight line, and then apply it to the rate equation of a Michaelis-Menten enzyme and a general polynomial. In each case the approximation is generally larger (and never smaller) than the corresponding standard confidence band, but in at least some instances the upper bound of the discrepancy is about 40%.

Keywords: confidence interval, interval arithmetic, Michaelis-Menten kinetics, polynomial.


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