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We fit theoretical models to the emission-line spectra of 2766 Seyfertgalaxies from the Sloan Digital Sky Survey (SDSS). The model line fluxes arederived by `mixing' photoionization model predictions of active galacticnucleus (AGN) narrow line region (NLR) emission and HII region emission. Theobserved line fluxes in each spectrum were directly compared to the grid ofmixed models using the Bayesian parameter estimation code NebulaBayes, therebymeasuring the degree of mixing in each spectrum for the first time. We findthat the majority of the Balmer line emission in the majority ofSeyfert-classified SDSS spectra arises from contaminating HII regions withinthe fixed-size aperture. Even for spectra with log [OIII]/Hb $\gtrsim 0.9$, amedian of ~30% of the Balmer flux arises in HII regions. We show that theresults are qualitatively insensitive to the assumed Seyfert ionizingcontinuum, and that ionizing spectra with a peak energy of E_peak ~ 40-50 eVproduce the most plausible distributions of mixing fractions. The analysiscleanly quantifies how the starburst - AGN `mixing fraction' increases on theBPT diagram for SDSS galaxies. Apart from the mixing fraction, the models alsovary with the ionization parameter in the NLR, the gas pressure, and themetallicity. Measurements for the metallicity in particular will be presentedin a companion paper.

Mixing between Seyfert and HII-region excitation in local active galaxies