By T. Bausch, M. Schwaiger (auth.), Professor Dr. Martin Schader (eds.)

ISBN-10: 3540547088

ISBN-13: 9783540547082

ISBN-10: 3642467571

ISBN-13: 9783642467578

The quantity comprises revised models of papers provided on the fifteenth Annual assembly of the "Gesellschaft f}r Klassifika- tion". Papers have been prepared within the following 3 elements that have been the most streams of debate throughout the confe- rence: 1. info research, category 2. info Modeling, wisdom Processing, three. functions, distinctive topics. New effects on constructing mathematical and statistical tools permitting quantitative research of knowledge are said on. instruments for representing, modeling, storing and processing da- ta and information are mentioned. functions in astro-phycics, archaelogy, biology, linguistics, and drugs are offered.

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Additional resources for Analyzing and Modeling Data and Knowledge: Proceedings of the 15th Annual Conference of the “Gesellschaft für Klassifikation e.V.“, University of Salzburg, February 25–27, 1991

Sample text

We call its density function "credibility distribution". t2, and 0'2 are assumed to be known. For class 1 we define: A _ U1",- 7r1 Lb 7r1Lb + 7r2L2", For class k = 2 the parameter d 2", is defined completely analog. tk, and the value of the likelihood function at the symptom value x is, again, given by L k", = (1/V2i) exp (-z~",/2) . t2,0'2) are known exactly and assume instead that the knowledge about the parameters is expressed by two probability density distributions. We will derive the conditional probability distribution of the credibility parameter given the previous experience E = (nl, n2; Xl, X2; s~, and the observed symptom value x.

E) Po :F PI Po :F PI, 0 < f < 1 (3)1 po :F PI, (3 > 1 where in the case D, Q. denotes the translation mixture f· Np(Po, E) + (1- f)' Np(Pl' E). ' which is either Fisher's discriminant function or some type of Mahalanobis distance. For our cases A to C, the special form of h(T) and T( x) is shown in Tab. (aT-bS2 -d) eT + (1- Fl f)e T N(-~,62) G[ X: (32. T~ 2 . 1) In the case D, G[ = f· N( -~, 62 ) + (1 - f) . N( +~, 62 ) is the mixture of two univariate normals. The monotonicity of the link function h(T) implies that the form of any optimal or any maximum-support-line partition C = {C1, ...

We now observe a new object which has the feature value x and we want to know from which class it comes from. We assume that the cases are assigned to the two classes according to a Bernoulli process with the parameters 7r and 1 - 7r. The parameters represent the base rates. , Indeed, if the sampling scheme fixes both n1 and n2, the sample does not contain information about the base rates. , p(XI/Lk' O"~) = N(/Lk,O"n ex exp ( -~ C 2), ::k) k = 1,2. and sampling is independent and identical. We denote by Lk the class-conditionallikelihood function and by Lk:r: its value at a fixed symptom value x.

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Analyzing and Modeling Data and Knowledge: Proceedings of the 15th Annual Conference of the “Gesellschaft für Klassifikation e.V.“, University of Salzburg, February 25–27, 1991 by T. Bausch, M. Schwaiger (auth.), Professor Dr. Martin Schader (eds.)

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