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    题名: Consistency of the Bayes method for the inverse scattering problem
    作者: 邱普照
    Kow, Pu-Zhao;Furuya, Takashi;Wang, Jenn-Nan
    贡献者: 應數系
    关键词: inverse scattering problem;Bayes method;consistency;contraction rate
    日期: 2024-03
    上传时间: 2024-05-24 11:34:16 (UTC+8)
    摘要: In this work, we consider the inverse scattering problem of determining an unknown refractive index from the far-field measurements using the nonparametric Bayesian approach. We use a collection of large 'samples', which are noisy discrete measurements taking from the scattering amplitude. We will study the frequentist property of the posterior distribution as the sample size tends to infinity. Our aim is to establish the consistency of the posterior distribution with an explicit contraction rate in terms of the sample size. We will consider two different priors on the space of parameters. The proof relies on the stability estimates of the forward and inverse problems. Due to the ill-posedness of the inverse scattering problem, the contraction rate is of a logarithmic type. We also show that such contraction rate is optimal in the statistical minimax sense.
    關聯: Inverse Problems, Vol.40, No.5, 055001
    数据类型: article
    DOI 連結: https://doi.org/10.1088/1361-6420/ad3089
    DOI: 10.1088/1361-6420/ad3089
    显示于类别:[應用數學系] 期刊論文

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