• Corpus ID: 235731512

# The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

@article{Shen2021TheEO,
title={The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models},
author={Yunyi Shen and Claudia R. Sol{\'i}s-Lemus},
journal={arXiv: Methodology},
year={2021}
}
• Published 2 July 2021
• Mathematics
• arXiv: Methodology
Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. We approximate the marginal posterior precision of the precision matrix via Laplace approximation under different priors: a flat prior, the conjugate prior Normal-Wishart, the unconfounded prior Normal-Matrix Generalized Inverse Gaussian (MGIG…

## References

SHOWING 1-10 OF 49 REFERENCES
Bayesian Conditional Auto-Regressive LASSO Models to Learn Sparse Networks with Predictors
• Computer Science
• 2020
A novel Bayesian conditional auto-regressive LASSO model is introduced to infer a sparse network structure with nodes for responses and for predictors and whose edges all represent conditional dependence, not conditional among responses and marginal between responses and predictors.
• Mathematics
• 1990
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory
Network analysis methods for studying microbial communities: A mini review
• Biology
Computational and structural biotechnology journal
• 2021
Differential associations between interpersonal variables and quality-of-life in a sample of college students
• Psychology
Quality of Life Research
• 2019
Results from this research suggest that interpersonal factors in general, and loneliness in particular, are strongly associated with quality-of-life.
Modelling approaches for studying the microbiome
• Biology
Nature Microbiology
• 2019
This Review summarizes mathematical modelling approaches that can be applied to microbiome datasets, providing insights into microbial dynamics and interactions in this complex system.
On Deriving the Inverse of a Sum of Matrices
• Mathematics
• 1981
Available expressions are reviewed and new ones derived for the inverse of the sum of two matrices, one of them being nonsingular. Particular attention is given to \$({\text{{\bf A}}} + {\text{{\bf
Exponential transformation models
• Mathematics, Computer Science
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
• 1982
It is shown, by using standard exponential family theory, that the group of transformations on the sample space generating the model induces affine transformation groups on the parameter space and on the range space of the minimal sufficient statistic, the induced groups being in fact representations of the original transformation group.
Estimation of a covariance matrix under Stein's loss
• Mathematics
• 1985
On decrit la technique generale de Stein pour ameliorer l'estimateur sans biais invariant le meilleur et l'estimateur minimax de la matrice de covariance normale