随机偏微分方程的普罗霍罗夫度量框架与总体数据反问题
THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs.
作者信息
Banks H T, Flores K B, Rosen I G, Rutter E M, Sirlanci Melike, Thompson W Clayton
机构信息
Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC, USA.
Department of Mathematics, University of Southern California, Los Angeles, CA, USA.
出版信息
Commun Appl Anal. 2018;22(3):415-446. Epub 2018 Jun 19.
Abstract
We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.
摘要
我们考虑在仅能获取总体（群体层面）数据的问题中对概率测度参数进行非参数估计。我们总结了一种针对估计问题的现有计算方法，该方法是在过去几十年中发展起来的[24, 5, 12, 28, 16]。给出了理论结果，这些结果确立了非常一般的（普通、广义及其他）最小二乘估计和估计量对于测度估计问题的存在性和一致性，并特别应用于随机偏微分方程。
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