It has been well recognized that the observed temperature changes consist of effects from anthropogenic forcings (e.g., greenhouse gases, land-use change), natural forcings (e.g., volcanic eruptions, solar activity), and internal natural variabilities (Eyring et al., 2021), but separating their contributions is challenging. Straightforwardly, one may achieve this by comparing observations with model simulations under different forcings, but this is limited by the ability of current coupled models in capturing the internal natural variability of the climate system (Fyfe et al., 2013). For example, many models missed the simulation of the recent global warming hiatus (GWH) from 1998 to 2012 (Papalexiou et al., 2020). In recent years, great efforts have been made in Detection and Attribution studies, and a sophisticated way is to carry out generalized linear regressions of model simulations against observational data, that is, the optimal fingerprinting (OFP) method (Allen & Tett, 1999;Hasselmann, 1997). The OFP method is able to distinguish the contributions of different factors on observed climate changes, but model simulations usually require massive computing resources and have uncertainties particularly on regional scales (Bindoff et al., 2013). To meet the demands of Detection and Attribution science, statistical approaches based solely on