Algebraic representation of Gaussian Markov combinations

Journal article

Markov combinations for structural meta-analysis problems provide a way of constructing a statistical model that takes into account two or more marginal distributions by imposing conditional independence constraints between the variables that are not jointly observed. This paper considers Gaussian distributions and discusses how the covariance and concentration matrices of the different combinations can be found via matrix operations. In essence all these Markov combinations correspond to finding a positive definite completion of the covariance matrix over the set of random variables of interest and respecting the constraints imposed by each Markov combination. The paper further shows the potential of investigating the properties of the combinations via algebraic statistics tools. An illustrative application will motivate the importance of solving problems of this type.

Authors: Massa, S; Riccomagno, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Bernoulli Society for Mathematical Statistics and Probability
• Journal: Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability
• Publication date: 2015-01-01
• DOI: 10.3150/15-BEJ759
• ISSN: 1573-9759
• Keywords: Markov combinations; Gaussian graphical models; algebraic statistics