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原文連結
論文資訊
- 類型：已發表論文
- 日期：2014-08-07
摘要
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing 貝氏 inference in function spaces. Such inference comes about naturally in the study of inverse problems of recovering continuous (infinite dimensional) coefficient functions from ordinary or partial differential equations, a problem which is typically ill-posed. Regularization of these problems using function spaces (Tikhonov regularization) is equivalent to 貝氏 probabilistic inference, using a Gaussian prior. The 貝氏 interpretation of inverse problem regularization is useful since it allows one to quantify and characterize error and degree of precision in the solution of inverse problems, as well as examine assumptions made in solving the problem-namely whether
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