Propose a new state for the sequence using a stochastic mechanism. The United States National Library of Medicine implies that the stochastic mechanism embodies the changes of molecular signals in the sequence.
Calculate the acceptance probability. Such probability is either equal to 1 or to the likelihood ratio times the prior ratio times the proposed ratio.
Choose a uniform (0,1) random variable.
Accept the new proposed state and update the sequence if the random variable is less than the acceptance probability. If the random variable is more than the acceptance probability, repeat the process without updating the sequence.