Resumen
We introduce a novel approach to estimate the temporal variation of the b-value parameter of the Gutenberg?Richter law, based on the weighted likelihood approach. This methodology allows estimating the b-value based on the full history of the available data, within a data-driven setting. We test this methodology against the classical ?rolling window? approach using a high-definition Italian seismic catalogue as well as a global catalogue of high magnitudes. The weighted likelihood approach outperforms competing methods, and measures the optimal amount of past information relevant to the estimation.