Algebraic representations of Gaussian Markov combinations

Markov combinations for structural meta-analysis problems provide a way of constructing a\udstatistical model that takes into account two or more marginal distributions by imposing condi-\udtional independence constraints between the variables that are not jointly observed. This paper\udconsiders Gaussian distributions and discusses how the covariance and concentration matrices\udof the dierent combinations can be found via matrix operations. In essence all these Markov\udcombinations correspond to nding a positive denite completion of the covariance matrix over\udthe set of random variables of interest and respecting the constraints imposed by each Markov\udcombination. The paper further shows the potential of investigating the properties of the com-\udbinations via algebraic statistics tools. An illustrative application will motivate the importance\udof solving problems of this type