Due to modern advances in computing power, the use of increasingly complex models has become practical. One class of large models that often relies on numerical techniques for parameter estimation is multi-resolution models. Unfortunately, numerical maximization and sampling techniques used to estimate parameters in such complex models often explore the parameter space slowly, resulting in unreliable or unstable estimates. This paper proposes a multi-resolution genetic algorithm that incorporates elements of simulated tempering to allow efficient estimation of parameters in multi-scale models. This algorithm can also be adapted to perform Markov chain Monte Carlo sampling from a posterior distribution in a Bayesian setting, which can greatly improve mixing and exploration of the posterior. Parallel implementation is addressed. These methods are demonstrated on examples from single photon emission computed tomography and groundwater hydrology. Keywords: Bayesian Statistics, Parallel Computing, Simulated Tempering, Evolutionary Monte Carlo

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