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Parameter estimation and the space of random variables

文献类型： 会议论文

第一作者： Andrea De Gaetano

作者： Andrea De Gaetano 1 ; Giulia Aliffi 2 ;

作者机构： 1.National Research Council (IRIB-CNR and IASI-CNR), Palermo and Rome, Italy|Dept. of Biomatics, óbuda University, Budapest, Hungary

2.Dipartimento di Matematica, Universitá Degli Studi di Catania, Catania, Italy

关键词： Manifolds;Geometry;Analytical models;Parameter estimation;Computational modeling;Minimization;Hilbert space

会议名称： IEEE International Conference on Intelligent Engineering Systems

主办单位：

页码： 263-268

摘要： The procedure of parameter estimation for nonlinear models, e.g. in biomedicine, is typically carried out by the minimization of a cost functional (e.g. Ordinary Least Squares, OLS) of the differences between predicted and experimentally observed values. As such, this process, of an exquisitely computational nature, is carried out in n-dimensional Euclidean space (case space). Theoretically, however, what is desired and what is indeed the philosophical essence of the modelling effort, is to approximate some hypothetical random variable expressing the possible outcomes of the process of interest with some other random variable, computable as a (very possibly nonlinear) function of more readily observable random variables. The aim of the present work is to describe the logical relationship between the Hilbert space of random variables and n-dimensional case space.

分类号： tp313

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