## Bernoulli

- Bernoulli
- Volume 23, Number 1 (2017), 626-644.

### Algebraic representations of Gaussian Markov combinations

M. Sofia Massa and Eva Riccomagno

#### Abstract

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.

#### Article information

**Source**

Bernoulli, Volume 23, Number 1 (2017), 626-644.

**Dates**

Received: November 2013

Revised: August 2015

First available in Project Euclid: 27 September 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1475001369

**Digital Object Identifier**

doi:10.3150/15-BEJ759

**Mathematical Reviews number (MathSciNet)**

MR3556787

**Zentralblatt MATH identifier**

1359.62281

**Keywords**

algebraic statistics conditional independence Gaussian graphical models Markov combinations

#### Citation

Massa, M. Sofia; Riccomagno, Eva. Algebraic representations of Gaussian Markov combinations. Bernoulli 23 (2017), no. 1, 626--644. doi:10.3150/15-BEJ759. https://projecteuclid.org/euclid.bj/1475001369