Data reconciliation of nonnormal observations with nonlinear constraints |
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Authors: | Oliver Cencic Rudolf Frühwirth |
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Institution: | 1. Institute for Water Quality, Resource and Waste Management, TU Wien, Wien, Austria;2. Institute of High Energy Physics (HEPHY), Austrian Academy of Sciences, Wien, Austria;3. Institute of Statistics and Mathematical Methods in Economics, TU Wien, Wien, Austria |
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Abstract: | This paper presents a new method for the reconciliation of data described by arbitrary continuous probability distributions, with the focus on nonlinear constraints. The main idea, already applied to linear constraints in a previous paper, is to restrict the joint prior probability distribution of the observed variables with model constraints to get a joint posterior probability distribution. Because in general the posterior probability density function cannot be calculated analytically, it is shown that it has decisive advantages to sample from the posterior distribution by a Markov chain Monte Carlo (MCMC) method. From the resulting sample of observed and unobserved variables various characteristics of the posterior distribution can be estimated, such as the mean, the full covariance matrix, marginal posterior densities, as well as marginal moments, quantiles, and HPD intervals. The procedure is illustrated by examples from material flow analysis and chemical engineering. |
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Keywords: | Data reconciliation Bayesian approach nonlinear constraints nonnormal distributions Markov chain Monte Carlo |
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