2013
DOI: 10.2478/msr-2013-0015
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A Formalism for Expressing the Probability Density Functions of Interrelated Quantities

Abstract: In this paper we address measurement problems involving several quantities that are interrelated by model equations. Available knowledge about some of these quantities is represented by probability density functions (PDFs), which are then propagated through the model in order to obtain the PDFs attributed to the quantities for which nothing is initially known. A formalism for analyzing such models is presented. It comprises the concept of a "base parameterization", which is used in conjunction with the change-… Show more

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Cited by 6 publications
(7 citation statements)
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“…Cavitation number depends on the geometry of the region where cavitation is expected to occur [14], [17], [18], so it can only be determined by measurement.…”
Section: Cavitation Numbermentioning
confidence: 99%
“…Cavitation number depends on the geometry of the region where cavitation is expected to occur [14], [17], [18], so it can only be determined by measurement.…”
Section: Cavitation Numbermentioning
confidence: 99%
“…where m < n. Using bold letters as a short notation for the totality of items in a set, these equations can be condensed into f .X / D 0. If the functions f .i / are compatible, independent of one another and sufficiently well-behaved, selections of n m quantities exist that suffice to express the complete state of knowledge (Lira & Grientschnig, 2013). Such a subset of quantities represents a coordinate system or parameterization.…”
Section: Terms and Symbolsmentioning
confidence: 99%
“…The answer to this question was given in [6], a summary of which is provided in Section II. But before going into details let us clarify the meaning of the question.…”
Section: Introductionmentioning
confidence: 99%
“…The sequence of our treatment is as follows. In Section II we summarize the formalism in [6] for expressing the PDFs for interrelated quantities. The formalism is based on the change-of-variables theorem, and its output is a joint PDF for some or all of the quantities that were initially unknown.…”
Section: Introductionmentioning
confidence: 99%