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Full-Text Articles in Physical Sciences and Mathematics
Fuzziness And Bayesian Analysis In Engineering, Matthias Stein, Michael Beer, Vladik Kreinovich
Fuzziness And Bayesian Analysis In Engineering, Matthias Stein, Michael Beer, Vladik Kreinovich
Departmental Technical Reports (CS)
An engineering analysis requires a realistic quantification of all input information. The amount and quality of the available information dictates the uncertainty model and its associated quantification concept. For inconsistent information, a distinction between probabilistic and non-probabilistic characteristics is beneficial. In this distinction, uncertainty refers to probabilistic characteristics and non-probabilistic characteristics are summarized as imprecision. When uncertainty and imprecision occur simultaneously, the uncertainty model fuzzy randomness appears useful. In a Bayesian approach the fuzzy probabilistic model provides the opportunity to take account of imprecision in data and in prior expert knowledge. The Bayesian approach ex-tended to inconsistent information is demonstrated …
Bayesian Approach For Inconsistent Information, M. Stein, Michael Beer, Vladik Kreinovich
Bayesian Approach For Inconsistent Information, M. Stein, Michael Beer, Vladik Kreinovich
Departmental Technical Reports (CS)
In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the {\it exact} sample values, that the prior distribution is {\it exactly} known, etc. In reality, the data is imprecise due to measurement errors, the …