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A novel method for extracting multipole amplitudes in the nucleon resonance region from electroproduction data is presented. The method is based on statistical concepts and it relies heavily on Monte Carlo and simulation techniques; it produces precise identification and determination of the contributing multipole amplitudes in the resonance region and for the first time a rigorous determination of the associated experimental uncertainty. The results are demonstrated to be independent of any model bias. The method is applied in the reanalysis of the Bates and Mainz $N\to \Delta$ data.

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