The methods of the previous chapter are useful for employing a multiscale approach for computational efficiency but are not as useful when one is faced with truly multiscale data. In contrast, the methods in this chapter are equally useful as a computational tool or for a full analysis of multiscale data. These methods can be seen as a generalization of simulated sintering, where instead of having a single chain moving between scales, multiple chains are run so that there is one (or more) chain at each scale at each point in time. These chains periodically exchange scales with each other, which allows information to move across scales but also ensures that we continue to sample at every scale. This eliminates some of the difficulties in posterior inference that can occur when trying to incorporate samples which are disjoint in time. In particular, simulated sintering produces a single MCMC run over the joint space of the parameters and the scale, but for any particular scale, there will only be MCMC samples at unconnected intervals.
KeywordsCoarse Scale Acceptance Probability Multiscale Approach Gaussian Process Model Posterior Inference
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