A method for determining a probabilistic model configured to predict a characteristic (e.g., defects, CD, etc.) of a pattern of a substrate subjected to a patterning process. The method includes obtaining a spatial map of a distribution of a residue corresponding to a characteristic of the pattern on the substrate, determining a zone of the spatial map based on a variation of the distribution of the residue within the spatial map, and determining the probabilistic model based on the zone and the distribution of the residue values or the values of the characteristic of the pattern on the substrate within the zone.