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Ions in the F region ionosphere at 150–400 km altitude consist mainly of molecular NO+ and O2+ ${\mathrm{O}}_{2}^{+}$, and atomic O+. Incoherent scatter (IS) radars are sensitive to the molecular‐to‐atomic ion density ratio, but its effect to the observed incoherent scatter spectra is almost identical with that of the ion temperature. It is thus very difficult to fit both the ion temperature and the fraction of O+ ions to the observed spectra. In this paper, we introduce a novel combination of Bayesian filtering, smoothness priors, and chemistry modeling to solve for F1 region O+ ion fraction from EISCAT Svalbard IS radar (75.43° corrected geomagnetic latitude) data during the international polar year (IPY) 2007–2008. We find that the fraction of O+ ions in the F1 region ionosphere is controlled by ion temperature and electron production. The median value of the molecular‐to‐atomic ion transition altitude during IPY varies from 187 km at 16–17 MLT to 208 km at 04–05 MLT. The ion temperature has maxima at 05–06 MLT and 15–16 MLT, but the transition altitude does not follow the ion temperature, because photoionization lowers the transition altitude. A daytime transition altitude maximum is observed in winter, when lack of photoionization leads to very low daytime electron densities. Both ion temperature and the molecular‐to‐atomic ion transition altitude correlate with the Polar Cap North geomagnetic index. The annual medians of the fitted transition altitudes are 14–32 km lower than those predicted by the International Reference Ionosphere. Plain Language Summary: Ions in the F region ionosphere at 150–400 km altitudes consist mainly of molecular NO+ and O2+ ${\mathrm{O}}_{2}^{+}$, and atomic O+. Incoherent scatter radars are sensitive to the molecular‐to‐atomic ion density ratio, but its effect to the observed incoherent scatter spectra is almost identical with that of the ion temperature. It is thus very difficult to fit both the ion temperature and the fraction of O+ ions to the observed spectra. This causes bias to the fitted temperatures and leaves behavior of the F1 region ion composition poorly known. We apply a novel combination of inverse mathematics and chemistry modeling to analysis of EISCAT Svalbard incoherent scatter radar data, and solve for both the ion temperature and the fraction of O+ ions at the same time. We find that the ion composition is considerably different from a standard model, that it undergoes regular diurnal variations, and it is affected by geomagnetic activity. The typical variations can be qualitatively explained by known diurnal variations in ion temperature, solar photoionization, and ion chemistry. When the ionosphere above Svalbard is in almost complete darkness in mid‐winter, ion composition in the daytime ionosphere is considerably different from that observed during the other seasons. Key Points: We use novel data analysis techniques and chemistry modeling to fit atomic oxygen ion fractions to EISCAT Svalbard radar data during IPYWe characterize the F1 region ion composition dependence on local time, solar zenith angle, and geomagnetic activityThe molecular‐to‐atomic ion transition altitudes are 14–32 km lower than those predicted by the International Reference Ionosphere [ABSTRACT FROM AUTHOR]