Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is often a function of expensive computations, such as a high-fidelity physical simulation, an intractable integral, or a slowly-converging iterative algorithm. Thus, using an MCMC algorithms with an expensive target density becomes impractical, as these expensive computations need to be evaluated at each iteration of the algorithm. In practice, these computations often approximated via a cheaper, low-fidelity computation, leading to bias in the resulting target density. Multi-fidelity MCMC algorithms combine models of varying fidelities in order to obtain an approximate target density with lower computational cost. In this paper, we describe a class of asymptotically exact multi-fidelity MCMC algorithms for the setting where a sequence of models of increasing fidelity can be computed that approximates the expensive target density of interest. We take a pseudo-marginal MCMC approach for multi-fidelity inference that utilizes a cheaper, randomized-fidelity unbiased estimator of the target fidelity constructed via random truncation of a telescoping series of the low-fidelity sequence of models. Finally, we discuss and evaluate the proposed multi-fidelity MCMC approach on several applications, including log-Gaussian Cox process modeling, Bayesian ODE system identification, PDE-constrained optimization, and Gaussian process regression parameter inference.
翻译:Markov 链的 Monte Carlo (MCMC) 是科学应用中不确定性量化和传播的既定方法。 在应用 MCMC 在科学领域应用 MMC 方面的一个关键挑战是计算: 目标利息密度往往是昂贵的计算方法, 如高纤维物理模拟、 棘手的有机体, 或缓慢趋同的迭接算法。 因此, 使用成本高目标密度的 MC 算法变得不切实际, 这些昂贵的计算方法需要在算法的每次迭代中进行评估。 实际上, 这些计算方法往往通过更便宜、 低纤维性计算, 导致目标密度的偏差。 多纤维性 MMC 算法将不同忠诚的模型结合在一起, 以较低的计算成本密度。 在本文中, 我们描述了一组非同步性的多纤维性多纤维化的计算方法, 高度的计算方法, 高度的精确度评估方法, 高度的计算方法, 接近昂贵的目标密度的计算方法 。 我们用模拟的MC MC 方法, 多纤维性应用, 以更廉价的精确性 的序列 。