  We describe a general strategy for sampling configurations from a given
distribution, NOT based on the standard Metropolis (Markov chain) strategy. It
uses the fact that nontrivial problems in statistical physics are high
dimensional and often close to Markovian. Therefore, configurations are built
up in many, usually biased, steps. Due to the bias, each configuration carries
its weight which changes at every step. If the bias is close to optimal, all
weights are similar and importance sampling is perfect. If not, ``population
control" is applied by cloning/killing partial configurations with too high/low
weight. This is done such that the final (weighted) distribution is unbiased.
We apply this method (which is also closely related to diffusion type quantum
Monte Carlo) to several problems of polymer statistics, reaction-diffusion
models, sequence alignment, and percolation.
