Density Elicitation with applications in Probabilistic Loops
| Autor: | Kofnov, Andrey, Bartocci, Ezio, Bura, Efstathia |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Probabilistic loops can be employed to implement and to model different processes ranging from software to cyber-physical systems. One main challenge is how to automatically estimate the distribution of the underlying continuous random variables symbolically and without sampling. We develop an approach, which we call K-series estimation, to approximate statically the joint and marginal distributions of a vector of random variables updated in a probabilistic non-nested loop with polynomial and non-polynomial assignments. Our approach is a general estimation method for an unknown probability density function with bounded support. It naturally complements algorithms for automatic derivation of moments in probabilistic loops such as~\cite{BartocciKS19,Moosbruggeretal2022}. Its only requirement is a finite number of moments of the unknown density. We show that Gram-Charlier (GC) series, a widely used estimation method, is a special case of K-series when the normal probability density function is used as reference distribution. We provide also a formulation suitable for estimating both univariate and multivariate distributions. We demonstrate the feasibility of our approach using multiple examples from the literature. Comment: 34 pages |
| Databáze: | arXiv |
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