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We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the corresponding values are known only up to measurement errors having some assumed distribution and correlation structure. The method, Moving Taylor Bayesian Regression (MOTABAR), uses Bayesian updating to find the posterior mean of the coefficients of a Taylordoi:10.1137/12087846x fatcat:fygde4jxi5ffdnbcopqqs62eou