A general framework for data reconciliation—Part I: Linear constraints

• General framework for data reconciliation of nonnormally distributed data.
• Monte Carlo Markov Chain algorithm based on an independence sampler.
• Graphical and numerical examples.

This paper presents a new method, based on Bayesian reasoning, for the reconciliation of data from arbitrary probability distributions. The main idea is to restrict the joint prior probability distribution of the involved variables with model constraints to get a joint posterior probability distribution. This paper covers the case of linearly constrained variables, with the focus on equality constraints. The procedure is demonstrated with the help of three simple graphical examples. Because in general the posterior probability density function cannot be calculated analytically, it is sampled with a Markov chain Monte Carlo (MCMC) method. From this sample the density and its moments can be estimated, along with the marginal densities, moments and quantiles. The method is tested on several artificial examples from material flow analysis, using an independence Metropolis–Hastings sampler.