The article investigates the processing and analysis of nonlinear random equation systems, where the parameters are modeled as random variables. The key points are:
General derivation of the likelihood function and posterior density for the approximate solutions of the random equation systems, without significant restrictions on the type of nonlinearity or mixture models.
Demonstration of the high combinatorial potential when using mixture model parameter random variables, by analyzing the number of possible equation system combinations.
Presentation of numerical techniques, such as Monte Carlo integration, to efficiently evaluate the likelihood function for high-dimensional equations.
Simulation examples showcasing the application of the methodology to random linear equation systems, nonlinear conic section equations, portfolio optimization, control engineering, and random matrix theory.
The article highlights the practical relevance of the presented framework for the applied researcher, providing a general and inclusive approach to processing and analyzing nonlinear random equation systems.
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arxiv.org
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