This chapter starts by reviewing the key ideas of genetic algorithms and then demonstrates how to use them in a multiscale setting. The direct extension to multiscale modeling is useful for maximization. However, these multiscale ideas can also be extended to the Bayesian framework in combination with Markov chain Monte Carlo ideas. The resulting approach can then be seen as a generalization of the Metropolis-coupled methods of the previous chapter. This combination is a powerful method for fully Bayesian multiscale modeling, particularly in a parallel computing environment. Compared with the methods in the previous two chapters, the key extension of this chapter is to allow the swapping across scales (or “temperatures”) of only part of the information in the chains instead of requiring the entire current state of the chain to move between scales. This adaptation can improve the probability of accepting a swap in complicated problems and thus further improve the mixing of the chains.
KeywordsGenetic Algorithm Markov Chain Monte Carlo Solution Vector Markov Chain Monte Carlo Algorithm Previous Chapter
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