南方科技大学知识苑(SUSTech KC): A posterior contraction for Bayesian inverse problems in Banach spaces

题名	A posterior contraction for Bayesian inverse problems in Banach spaces
作者	Chen，De Han 1; Li，Jingzhi2 ; Zhang，Ye 3,4
通讯作者	Zhang，Ye
发表日期	2024-04-01
DOI	10.1088/1361-6420/ad2a03
发表期刊	Inverse Problems 影响因子和分区
ISSN	0266-5611
EISSN	1361-6420
卷号	40 期号:4
摘要	This paper features a study of statistical inference for linear inverse problems with Gaussian noise and priors in structured Banach spaces. Employing the tools of sectorial operators and Gaussian measures on Banach spaces, we overcome the theoretical difficulty of lacking the bias-variance decomposition in Banach spaces, characterize the posterior distribution of solution though its Radon-Nikodym derivative, and derive the optimal convergence rates of the corresponding square posterior contraction and the mean integrated square error. Our theoretical findings are applied to two scenarios, specifically a Volterra integral equation and an inverse source problem governed by an elliptic partial differential equation. Our investigation demonstrates the superiority of our approach over classical results. Notably, our method achieves same order of convergence rates for solutions with reduced smoothness even in a Hilbert setting.
关键词	Banach spaces Bayesian inverse problems convergence rates posterior contraction
相关链接	[Scopus记录]
收录类别	SCI ; EI
语种	英语
学校署名	其他
ESI学科分类	PHYSICS
Scopus记录号	2-s2.0-85186354851
来源库	Scopus
引用统计	被引频次[WOS]：2
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/729099
专题	理学院_数学系深圳国际数学中心（杰曼诺夫数学中心）（筹）理学院_深圳国家应用数学中心
作者单位	1.School of Mathematics and Statistics,Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan,430079,China 2.Department of Mathematics,National Center for Applied Mathematics Shenzhen & SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China 3.Shenzhen MSU-BIT University,Shenzhen,518172,China 4.School of Mathematics and Statistics,Beijing Institute of Technology,Beijing,100081,China
推荐引用方式 GB/T 7714	Chen，De Han,Li，Jingzhi,Zhang，Ye. A posterior contraction for Bayesian inverse problems in Banach spaces[J]. Inverse Problems,2024,40(4).
APA	Chen，De Han,Li，Jingzhi,&Zhang，Ye.(2024).A posterior contraction for Bayesian inverse problems in Banach spaces.Inverse Problems,40(4).
MLA	Chen，De Han,et al."A posterior contraction for Bayesian inverse problems in Banach spaces".Inverse Problems 40.4(2024).