Extraction of physical laws from joint experimental data

I. Grabec ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2005, vol. 48, issue 2, 279-289

Abstract: The extraction of a physical law y=y o (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 y o (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 y o (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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1140/epjb/e2005-00391-0 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:48:y:2005:i:2:p:279-289

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2005-00391-0

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().