Extraction of physical laws from joint experimental data
Grabec, Igor (Author)

URLURL - Presentation file, Visit http://dx.doi.org/10.1140/epjb/e2005-00391-0 New window

The extraction of a physical law y=yo(x) from joint experimental data about x and y is treated. The joint, the marginal and the conditional probability density functions (PDF) are expressed by given data over an estimator whose kernel is the instrument scattering function. As an optimal estimator of yo(x)the conditional average is proposed. The analysis of its properties is based upon a new definition of prediction quality. The joint experimental information and the redundancy of joint measurements are expressed by the relative entropy. With the number of experiments the redundancy on average increases, while the experimental information converges to a certain limit value. The difference between this limit value and the experimental information at a finite number of data represents the discrepancy between the experimentally determined and the true properties of the phenomenon. The sum of the discrepancy measure and the redundancy is utilized as a cost function. By its minimum a reasonable number of data for the extraction of the law yo(x)is specified. The mutual information is defined by the marginal and the conditional PDFs of the variables. The ratio between mutual information and marginal information is used to indicate which variable is the independent one. The properties of the introduced statistics are demonstrated on deterministically and randomly related variables.

Keywords:information science, communication theory, measurement, error theory, probability theory, stochastic processes, statistics
Work type:Not categorized (r6)
Tipology:1.01 - Original Scientific Article
Organization:FS - Faculty of Mechanical Engineering
Number of pages:str. 279-289
Numbering:Letn. 48, št. 2
ISSN on article:1434-6028
COBISS.SI-ID:8762651 Link is opened in a new window
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Record is a part of a journal

Title:#The #European physical journal
Shortened title:Eur. phys. j., B Cond. matter phys.
Publisher:EDP Sciences, Springer-Verlag
COBISS.SI-ID:13503271 New window

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