The spatial variability of the magnitude-frequency distribution is important to improve earthquake forecasting capabilities at different time scales. Here, we develop a novel approach, based on the weighted maximum-likelihood estimation, to build a spatial model for the b-value parameter of the Gutenberg-Richter law and its uncertainty, also for earthquake catalogs with a time-varying completeness magnitude. Then, we also provide a guideline based on the Bayes factor to measure the importance of the b-value spatial variability with respect to a model having a spatially uniform b-value. Finally, we apply the procedure to a new Italian instrumental earthquake catalog from 1960 to 2019 to investigate the b-value spatial variability over the Italian territory.
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