基于并行渐近独立马尔可夫抽样的高斯过程超参数估计
Gaussian process hyper-parameter estimation using parallel asymptotically independent Markov sampling
摘要：
计算上昂贵的计算机代码的高斯过程仿真器提供快速的统计近似来模拟物理过程。这些代理的训练取决于选择运行模拟器的设计点集。由于计算成本，这样的训练集必然是有限的，并且通过单峰分布量化仿真器的超参数中产生的不确定性可能会引起偏差。为了量化这种不确定性，本文提出了一种计算效率高的采样器的基础上扩展的渐近独立马尔可夫抽样，最近开发的算法贝叶斯推断。仿真器的结构不确定性作为超参数的贝叶斯处理的副产品而获得。此外，用户可以选择执行随机优化，以从最大后验估计的邻域中采样，即使在存在多模态的情况下也是如此。模型的不确定性也承认通过数值稳定措施，包括一个块金长期制定的概率模型。所提出的采样器的效率示出的例子中遇到的多模态分布。为了重复性、进一步开发和在其他应用中使用，用于生成示例的代码可在https://github.com/agarbuno/paims_codes免费下载
英文摘要：
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator. Due to computational cost, such training set is bound to be limited and quantifying the resulting uncertainty in the hyper-parameters of the emulator by uni-modal distributions is likely to induce bias. In order to quantify this uncertainty, this paper proposes a computationally efficient sampler based on an extension of Asymptotically Independent Markov Sampling, a recently developed algorithm for Bayesian inference. Structural uncertainty of the emulator is obtained as a by-product of the Bayesian treatment of the hyper-parameters. Additionally, the user can choose to perform stochastic optimisation to sample from a neighbourhood of the Maximum a Posteriori estimate, even in the presence of multimodality. Model uncertainty is also acknowledged through numerical stabilisation measures by including a nugget term in the formulation of the probability model. The efficiency of the proposed sampler is illustrated in examples where multi-modal distributions are encountered. For the purpose of reproducibility, further development, and use in other applications the code used to generate the examples is freely available for download at https://github.com/agarbuno/paims_codes
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
