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Abstract:
I describe two general methods for obtaining efficient Markov chain
Monte Carlo methods - temporarily mapping to a new space, which may be
larger or smaller than the original, and caching the results of
previous computations for re-use. These methods can be combined to
improve efficiency for problems where probabilities can be quickly
recomputed when only a subset of `fast' variables have changed. In
combination, these methods also allow one to effectively adapt tuning
parameters, such as the stepsize of random-walk Metropolis updates,
without actually changing the Markov chain transitions used, thereby
avoiding the issue that changing the transitions could undermine
convergence to the desired distribution. Temporary mapping and
caching can be applied in many other ways as well, offering a wide
scope for development of useful new MCMC methods.