In Bayesian inference, many problems can be expressed as the evaluation of the expectation of an uncertain quantity of interest with respect to the posterior distribution based on relevant data. Standard Monte Carlo method is often not applicable because the encountered posterior distributions cannot be sampled directly. In this case, the most popular strategies are the importance sampling method, Markov chain Monte Carlo, and annealing. In this paper, we introduce a new scheme for Bayesian inference, called Asymptotically Independent Markov Sampling (AIMS), which is based on the above methods. The efficiency of AIMS is demonstrated with an example that involves a multi-modal target distribution.
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