The purpose of this work is to better understand the confidence limits of the photospheric solar oxygen abundance derived from three-dimensional models using the forbidden [OI] line at 6300 $\AA{}$ , including correlations with other parameters involved. We worked with a three-dimensional empirical model and two solar intensity atlases. We employed Bayesian inference as a tool to determine the most probable value for the solar oxygen abundance given the model chosen. We considered a number of error sources, such as uncertainties in the continuum derivation, in the wavelength calibration and in the abundance/strength of Ni. Our results shows correlations between the effects of several parameters employed in the derivation. The Bayesian analysis provides robust confidence limits taking into account all of these factors in a rigorous manner. We obtain that, given the empirical three-dimensional model and the atlas observations employed here, the most probable value for the solar oxygen abundance is $\log(\epsilon_O) = 8.86\pm0.04$. However, we note that this uncertainty does not consider possible sources of systematic errors due to the model choice.