Data fusion using Hilbert space multi-dimensional models

General procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, built from quantum probability theory, are presented. HSM models can be applied to collections of K different contingency tables obtained from a set of p variables that are measured under different contexts. A context is defined by the measurement of a subset of the p variables that are used to form a table. HSM models provide a representation of the collection of K tables in a low dimensional vector space, even when no single joint probability distribution across the p variables exists. HSM models produce parameter estimates that provide a simple and informative interpretation of the complex collection of tables. (C) 2018 Elsevier B.V. All rights reserved.