ASYMPTOTICALLY INDEPENDENT MARKOV SAMPLING: A NEW MARKOV CHAIN MONTE CARLO SCHEME FOR BAYESIAN INFERENCE

被引:33
作者
Beck, James L. [1 ]
Zuev, Konstantin M. [1 ]
机构
[1] CALTECH, Dept Comp & Math Sci, Div Engn & Appl Sci, Pasadena, CA 91125 USA
基金
美国国家科学基金会;
关键词
Bayesian inference; uncertainty quantification; Markov chain Monte Carlo; importance sampling; simulated annealing; HIGH DIMENSIONS; DISTRIBUTIONS; SIMULATION; MODELS; PROBABILITIES;
D O I
10.1615/Int.J.UncertaintyQuantification.2012004713
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
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. 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.
引用
收藏
页码:445 / 474
页数:30
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