It then picks a possible change in the parameters and computes . If , then the change is accepted. After hundreds of such iterations, the distribution of accepted values of will converge to provided that all possible are eventually accessible. Parameter space is thus sampled with a density proportional to the likelihood. The trial changes are chosen at random.
Temperature control is thus an important element of the Metropolis.
The temperature control scheme must allow the search to sample the largest volume in parameter space with the lowest possible number of steps. After this initial cooling, the search continues. The ratio of the number of accepted over the number of trial is computed after every ten trials. If less than half the changes have been accepted, then the parameter temperatures are all decreased by 30 . If not, then the parameter temperatures are all increased by 30 .