NDLI: Adding Constraints to Situations When, In Addition to Intervals,We Also Have Partial Information about Probabilities

Content Provider	IEEE Xplore Digital Library
Author	Ceberio, M. Kreinovich, V. Gang Xiang Ferson, S. Joslyn, C.
Copyright Year	2006
Description	Author affiliation: Univ. of Texas at El Paso, El Paso (Ceberio, M.; Kreinovich, V.; Gang Xiang)
Abstract	In many practical situations, we need to combine probabilistic and interval uncertainty. For example, we need to 1 A compute statistics like population mean E = $1/n.^{n}Sigma_{i=1}x_{i}$ or population variance V = $1/n^{n}Sigma_{i=1}(x_{i}-E)^{2}$ in situations when we only know intervals $x_{i}$ of possible value of $x_{i}.$ In this case, it is desirable to compute the range of the corresponding characteristic. Some range computation problems are NP-hard; for these problems, in general, only an enclosure is possible. For other problems, there are efficient algorithms. In many practical situations, we have additional information that can be used as constraints on possible cumulative distribution functions (cdfs). For example, we may know that the actual (unknown) cdf is Gaussian. In this paper, we show that such constraints enable us to drastically narrow down the resulting ranges - and sometimes, transform the originally intractable (NP-hard) computational problem of computing the exact range into an efficiently solvable one. This possibility is illustrated on the simplest example of an NP-problem from interval statistics: the problem of computing the range V of the variance V. We also describe how we can estimate the amount of information under such combined intervals-and-constraints uncertainty.
Starting Page	30
Ending Page	30
File Size	141279
Page Count	1
File Format	PDF
DOI	10.1109/SCAN.2006.7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-09-26
Publisher Place	Germany
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Computer science Measurement errors Uncertainty Data analysis Statistical analysis Statistical distributions Data processing Statistics Distribution functions Postal services
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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