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This work combines experimental data from baryon spectroscopy with the latest statistical analysis-methods. The results are model-independent estimates of electromagnetic multipole parameters from which model-independent predictions of yet unmeasured polarization observables were calculated for the reaction γp → ηp, slightly above production threshold. For this purpose, truncated partial-wave analysis is combined with Bayesian inference for the first time. Thus, all results are given as distributions in contrast to point-estimates, which allows for an unprecedented uncertainty estimation.