The spatial correlation of coseismic slip is a necessary input for generating stochastic seismic rupture models, which are commonly used in seismic and tsunami hazard assessments. To date, the spatial correlation of individual earthquakes is characterized using finite fault models by finding the combination of parameters of a von K & aacute;rm & aacute;n autocorrelation function that best fits the observed autocorrelation function of the finite fault model. However, because a priori spatial correlation conditions (i.e. not in the data) are generally applied in finite fault model generation, the results obtained using this method may be biased. Additionally, robust uncertainty estimates for spatial correlations of coseismic slip are generally not performed. Considering these limitations in the classic method, here, a method is developed based on a Bayesian formulation of Finite Fault Inversion (FFI) with positivity constraints. This method allows for characterizing the spatial correlation of coseismic slip and its uncertainties for an earthquake by using samples of coseismic slip from a posterior probability density function (PDF). Furthermore, a Bayesian model selection criterion called Akaike Bayesian Information Criterion (ABIC) is applied to objectively choose between different prior spatial correlation schemes before computing the posterior, to reduce subjectivity due to this prior condition. The ABIC is calculated using an approximate analytical expression of Bayesian evidence. The method is applied to simulated P waves, demonstrating that model selection allows for objectively estimating the most suitable prior spatial correlation scheme in FFI. Additionally, the target spatial correlation of coseismic slip is accurately recovered using samples from the posterior PDF, as well as their uncertainties. Moreover, in the simulated experiment, it is shown that a non-robust choice of the prior spatial correlation scheme can significantly bias the estimated spatial correlations of coseismic slip. We apply our method to observed P waves from the 2015, Illapel earthquake ($M_{\rm w} = 8.3$), finding that the spatial correlation of coseismic slip of this earthquake is better described by a von K & aacute;rm & aacute;n ACF, with mean correlation lengths of around 47 km and Hurst parameter of 0.58. We conclude that using our method reduces biases associated with prior spatial correlation conditions and allows for robust estimation of spatial correlations of coseismic slip and their uncertainties.