Ions in the F region ionosphere at 150-400 km altitude consist mainly of molecular NO+ and O2+, 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.