Siam-Asa Journal on Uncertainty Quantification最新文献_第5页

Theoretical Guarantees for the Statistical Finite Element Method 统计有限元法的理论保证

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-11-30 DOI: 10.1137/21m1463963

Yanni Papandreou, Jon Cockayne, Mark Girolami, Andrew Duncan

引用次数: 1

Quantification of Errors Generated by Uncertain Data in a Linear Boundary Value Problem Using Neural Networks 线性边值问题中不确定数据误差的神经网络量化

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-11-28 DOI: 10.1137/22m1538855

Vilho Halonen, Ilkka Pölönen

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引用次数: 0

Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation 高斯过程插值中平滑参数估计的渐近界

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-11-27 DOI: 10.1137/22m149288x

Toni Karvonen

{"title":"Asymptotic Bounds for Smoothness Parameter Estimates in Gaussian Process Interpolation","authors":"Toni Karvonen","doi":"10.1137/22m149288x","DOIUrl":"https://doi.org/10.1137/22m149288x","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1225-1257, December 2023. <br/> Abstract. It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Matérn covariance kernel. The smoothness parameter of a Matérn kernel determines many important properties of the model in the large data limit, including the rate of convergence of the conditional mean to the response function. We prove that the maximum likelihood estimate of the smoothness parameter cannot asymptotically undersmooth the truth when the data are obtained on a fixed bounded subset of [math]. That is, if the data-generating response function has Sobolev smoothness [math], then the smoothness parameter estimate cannot be asymptotically less than [math]. The lower bound is sharp. Additionally, we show that maximum likelihood estimation recovers the true smoothness for a class of compactly supported self-similar functions. For cross-validation we prove an asymptotic lower bound [math], which, however, is unlikely to be sharp. The results are based on approximation theory in Sobolev spaces and some general theorems that restrict the set of values that the parameter estimators can take.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Sensitivity Analysis of Quasi-Stationary Distributions (QSDs) of Mass-Action Systems 质量-作用系统准平稳分布的灵敏度分析

3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-10-20 DOI: 10.1137/22m1535875

Yao Li, Yaping Yuan

引用次数: 0

An Order-Theoretic Perspective on Modes and Maximum A Posteriori Estimation in Bayesian Inverse Problems 贝叶斯反问题的模态和最大后验估计的序理论观点

3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-10-20 DOI: 10.1137/22m154243x

Hefin Lambley, T. J. Sullivan

引用次数: 5

Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs 随机输入线性椭圆偏微分方程最优控制的可靠误差估计

3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-10-18 DOI: 10.1137/22m1503889

Johannes Milz

引用次数: 0

Are Minimizers of the Onsager–Machlup Functional Strong Posterior Modes? 最小化的Onsager-Machlup功能强后验模式?

3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-10-10 DOI: 10.1137/23m1546579

Remo Kretschmann

{"title":"Are Minimizers of the Onsager–Machlup Functional Strong Posterior Modes?","authors":"Remo Kretschmann","doi":"10.1137/23m1546579","DOIUrl":"https://doi.org/10.1137/23m1546579","url":null,"abstract":"In this work we connect two notions: That of the nonparametric mode of a probability measure, defined by asymptotic small ball probabilities, and that of the Onsager-Machlup functional, a generalized density also defined via asymptotic small ball probabilities. We show that in a separable Hilbert space setting and under mild conditions on the likelihood, modes of a Bayesian posterior distribution based upon a Gaussian prior exist and agree with the minimizers of its Onsager-Machlup functional and thus also with weak posterior modes. We apply this result to inverse problems and derive conditions on the forward mapping under which this variational characterization of posterior modes holds. Our results show rigorously that in the limit case of infinite-dimensional data corrupted by additive Gaussian or Laplacian noise, nonparametric maximum a posteriori estimation is equivalent to Tikhonov-Phillips regularization. In comparison with the work of Dashti, Law, Stuart, and Voss (2013), the assumptions on the likelihood are relaxed so that they cover in particular the important case of white Gaussian process noise. We illustrate our results by applying them to a severely ill-posed linear problem with Laplacian noise, where we express the maximum a posteriori estimator analytically and study its rate of convergence in the small noise limit.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Fast Calibration for Computer Models with Massive Physical Observations 具有大量物理观测的计算机模型的快速校准

3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-09-27 DOI: 10.1137/22m153673x

Shurui Lv, Jun Yu, Yan Wang, Jiang Du

引用次数: 0

Bayesian Inference with Projected Densities 投影密度下的贝叶斯推断

3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-09-27 DOI: 10.1137/22m150695x

Jasper M. Everink, Yiqiu Dong, Martin S. Andersen

引用次数: 1

Dimension Free Nonasymptotic Bounds on the Accuracy of High-Dimensional Laplace Approximation 高维拉普拉斯近似精度的无维非渐近界

3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-09-27 DOI: 10.1137/22m1495688

Vladimir Spokoiny

引用次数: 0