If rejected, the sample stays the same. When the histogram for β is described as h β (e) and h β (e) ∝ n(e) exp(-βe). The DoS is thus obtained as n(e) ∝ h β (e) exp(βe). It amounts to assigning a weight proportional to exp(βe) to the samples whose failure rate is e. This method is called the single histogram method (SHM). Although SHM leads to better results than random sampling, it is still not very efficient due to the difficulty of MCMC sampling for large β. Since larger β leads to a smaller acceptance rate, it is necessary to prepare numerous proposals to obtain an acceptable sample. To avoid the problem, it is common to start from a small value of β and gradually increase it as done in simulated annealing and population annealing (PA). When annealing is applied, SHM cannot leverage all the samples, because only those for final temperature are used.