RT Journal Article ID 5fda50933d5a6c1a A1 Beck, James L. A1 Zuev, Konstantin M. T1 ASYMPTOTICALLY INDEPENDENT MARKOV SAMPLING: A NEW MARKOV CHAIN MONTE CARLO SCHEME FOR BAYESIAN INFERENCE JF International Journal for Uncertainty Quantification JO IJUQ YR 2013 FD 2013-03-12 VO 3 IS 5 SP 445 OP 474 K1 Bayesian inference K1 uncertainty quantification K1 Markov chain Monte Carlo K1 importance sampling K1 simulated annealing AB In Bayesian inference, many problems can he 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. We derive important ergodic properties of AIMS. In particular, it is shown that, under certain conditions, the AIMS algorithm produces a uniformly ergodic Markov chain. The choice of the free parameters of the algorithm is discussed and recommendations are provided for this choice, both theoretically and heuristically based. The efficiency of AIMS is demonstrated with three numerical examples, which include both multimodal and higher-dimensional target posterior distributions. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,2cb8d8b565b6c7f1,5fda50933d5a6c1a.html