The multiple histogram method (MHM) enables us to leverage all the samples across all temperatures. Let us assume that N i samples obtained at temperature β i , and denote the histograms with failure rate e as h i (e). If the SHM is applied separately, the weight of a β i -derived sample whose failure rate is e would be proportional to exp(β i e). Let us introduce a correction factor r i (e) to make it r i (e) exp(β i e). Under the assumption that the histogram counts are subject to Poisson distribution, the optimal values of r i (e) are derived in terms of free energy f i as