Hilbert space multidimensional modelling of continuous measurements

Data fusion problems arise when a researcher needs to analyse results obtained by measuring empirical variables under different measurement contexts. A context is defined by a subset of variables taken from a complete set of variables under investigation. Multiple contexts can be formed from different subsets, which produce a separate distribution of measurements associated with each context. A context effect occurs when the distributions produced by the different contexts cannot be reproduced by marginalizing over a complete joint distribution formed by all the variables. We propose a Hilbert space multidimensional theory that uses a state vector and measurement operators to account for multiple distributions produced by different contexts. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.