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February 2017 Algebraic representations of Gaussian Markov combinations
M. Sofia Massa, Eva Riccomagno
Bernoulli 23(1): 626-644 (February 2017). DOI: 10.3150/15-BEJ759


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.


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M. Sofia Massa. Eva Riccomagno. "Algebraic representations of Gaussian Markov combinations." Bernoulli 23 (1) 626 - 644, February 2017.


Received: 1 November 2013; Revised: 1 August 2015; Published: February 2017
First available in Project Euclid: 27 September 2016

zbMATH: 1359.62281
MathSciNet: MR3556787
Digital Object Identifier: 10.3150/15-BEJ759

Keywords: Algebraic statistics , Conditional independence , Gaussian graphical models , Markov combinations

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability


Vol.23 • No. 1 • February 2017
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