Resampling step of population annealing

I am trying to have a better understanding of the population annealing algorithm. In the section POPULATION ANNEALING, the steps of the algorithms are described. In Step 2 (Resampling (Split/Remove) of the replicas:), the new replica $$x^k_i$$ is resampled according to the probability $$p^k$$. So, what does it actually mean? Can I use a biased coin toss with the probability $$p^k$$ for heads and remove the replica if it is a tail?

• This would be much easier to answer if you gave more context, since the paper you reference is not publicly accessible. – noah May 21 at 14:13

The paper is rather explicit. It states that the weights $$W^k$$ are used to calculate the probability to resample a particular replica, $$P^k = W^k /(\sum_k W^k)$$. In particular it says, "Thus, a replica with a small weight $$W^k$$ is removed with a high probability, while a replica with a large weight tends to have multiple ''descendants''." Hence, your picture is correct, if you are interested only in the case whether or not a particular state resampled, because then a Binomial distribution is applicable. However, in general a better picture is that you have a urn with many balls and each ball has a number printed on it. The weights tell you how many balla have a particular number -- this is the multinomial distribution.