کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1156723 | 958860 | 2013 | 33 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems](/preview/png/1156723.png)
چکیده انگلیسی
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying the posterior using its precision operator. Working with the unbounded precision operator enables us to use partial differential equations (PDE) methodology to obtain rates of contraction of the posterior distribution to a Dirac measure centered on the true solution. Our methods assume a relatively weak relation between the prior covariance, noise covariance and forward operator, allowing for a wide range of applications.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 123, Issue 10, October 2013, Pages 3828–3860
Journal: Stochastic Processes and their Applications - Volume 123, Issue 10, October 2013, Pages 3828–3860
نویسندگان
Sergios Agapiou, Stig Larsson, Andrew M. Stuart,