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

Shen, Yunyi; Solís-Lemus, Claudia

doi:10.1007/s13253-024-00621-1

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

Journal Article · 30 April 2024 · Journal of Agricultural, Biological and Environmental Statistics

DOI: https://doi.org/10.1007/s13253-024-00621-1 · OSTI ID:2345078

Shen, Yunyi;

Abstract 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. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0021016

OSTI ID:: 2345078

Alternate ID(s):: OSTI ID: 2395885

Journal Information:: Journal of Agricultural, Biological and Environmental Statistics, Journal Name: Journal of Agricultural, Biological and Environmental Statistics; ISSN 1085-7117

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: United States

Language:: English

References (22)

Topological distortion and reorganized modular structure of gut microbial co-occurrence networks in inflammatory bowel disease Baldassano, Steven N.; Bassett, Danielle S. Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep26087	journal	May 2016
Log-determinant relaxation for approximate inference in discrete Markov random fields Wainwright, M. J.; Jordan, M. I. IEEE Transactions on Signal Processing, Vol. 54, Issue 6 https://doi.org/10.1109/TSP.2006.874409	journal	June 2006
Structure out of chaos: Functional brain network analysis with EEG, MEG, and functional MRI van Straaten, Elisabeth C. W.; Stam, Cornelis J. European Neuropsychopharmacology, Vol. 23, Issue 1 https://doi.org/10.1016/j.euroneuro.2012.10.010	journal	January 2013
Network analysis methods for studying microbial communities: A mini review Matchado, Monica Steffi; Lauber, Michael; Reitmeier, Sandra Computational and Structural Biotechnology Journal, Vol. 19 https://doi.org/10.1016/j.csbj.2021.05.001	journal	January 2021
Bayesian Graphical Lasso Models and Efficient Posterior Computation Wang, Hao Bayesian Analysis, Vol. 7, Issue 4 https://doi.org/10.1214/12-BA729	journal	December 2012
Bayesian Experimental Design: A Review Chaloner, Kathryn; Verdinelli, Isabella Statistical Science, Vol. 10, Issue 3 https://doi.org/10.1214/ss/1177009939	journal	August 1995
Complex network measures of brain connectivity: Uses and interpretations Rubinov, Mikail; Sporns, Olaf NeuroImage, Vol. 52, Issue 3 https://doi.org/10.1016/j.neuroimage.2009.10.003	journal	September 2010
Gut microbiota composition correlates with diet and health in the elderly Claesson, Marcus J.; Jeffery, Ian B.; Conde, Susana Nature, Vol. 488, Issue 7410 https://doi.org/10.1038/nature11319	journal	July 2012
The metagenomics RAST server – a public resource for the automatic phylogenetic and functional analysis of metagenomes Meyer, F.; Paarmann, D.; D'Souza, M. BMC Bioinformatics, Vol. 9, Issue 1 https://doi.org/10.1186/1471-2105-9-386	journal	September 2008
Food web patterns and their consequences Pimm, Stuart L.; Lawton, John H.; Cohen, Joel E. Nature, Vol. 350, Issue 6320 https://doi.org/10.1038/350669a0	journal	April 1991
Bayesian Regularization for Graphical Models With Unequal Shrinkage Gan, Lingrui; Narisetty, Naveen N.; Liang, Feng Journal of the American Statistical Association, Vol. 114, Issue 527 https://doi.org/10.1080/01621459.2018.1482755	journal	August 2018
Disentangling Interactions in the Microbiome: A Network Perspective Layeghifard, Mehdi; Hwang, David M.; Guttman, David S. Trends in Microbiology, Vol. 25, Issue 3 https://doi.org/10.1016/j.tim.2016.11.008	journal	March 2017
Estimation of a Covariance Matrix under Stein's Loss Dey, Dipak K.; Srinivasan, C. The Annals of Statistics, Vol. 13, Issue 4 https://doi.org/10.1214/aos/1176349756	journal	December 1985
Using network analysis to explore co-occurrence patterns in soil microbial communities Barberán, Albert; Bates, Scott T.; Casamayor, Emilio O. The ISME Journal, Vol. 6, Issue 2 https://doi.org/10.1038/ismej.2011.119	journal	September 2011
Nonconjugate Bayesian Estimation of Covariance Matrices and its Use in Hierarchical Models Daniels, Michael J.; Kass, Robert E. Journal of the American Statistical Association, Vol. 94, Issue 448 https://doi.org/10.1080/01621459.1999.10473878	journal	December 1999
The Matrix Generalized Inverse Gaussian Distribution: Properties and Applications Fazayeli, Farideh; Banerjee, Arindam Machine Learning and Knowledge Discovery in Databases https://doi.org/10.1007/978-3-319-46128-1_41	book	September 2016
Characterization of the Gut Microbiome Using 16S or Shotgun Metagenomics Jovel, Juan; Patterson, Jordan; Wang, Weiwei Frontiers in Microbiology, Vol. 7 https://doi.org/10.3389/fmicb.2016.00459	journal	April 2016
Chain Graph Models and their Causal Interpretations Lauritzen, Steffen L.; Richardson, Thomas S. Journal of the Royal Statistical Society Series B: Statistical Methodology, Vol. 64, Issue 3 https://doi.org/10.1111/1467-9868.00340	journal	August 2002
Bayesian Inference for the Spatial Random Effects Model Kang, Emily L.; Cressie, Noel Journal of the American Statistical Association, Vol. 106, Issue 495 https://doi.org/10.1198/jasa.2011.tm09680	journal	September 2011
Matrix Differential Calculus with Applications in Statistics and Econometrics Magnus, Jan R.; Magnus, Jan R. https://doi.org/10.1002/9781119541219	book	February 2019
Bayesian analysis of covariance matrices and dynamic models for longitudinal data Daniels, M. J. Biometrika, Vol. 89, Issue 3 https://doi.org/10.1093/biomet/89.3.553	journal	August 2002
On Deriving the Inverse of a Sum of Matrices Henderson, H. V.; Searle, S. R. SIAM Review, Vol. 23, Issue 1 https://doi.org/10.1137/1023004	journal	January 1981

Similar Records

B-PINNs: Bayesian Physics-informal Neural Networks for Forward and Inverse PDE Problems with Noisy Data

Journal Article · 2021 · Journal of Computational Physics · OSTI ID:1763962

Yang, Liu; Meng, Xuhui; Karniadakis, George E.

Minimally Informative Prior Distributions for PSA

Conference · 2010 · OSTI ID:984541

Kelly, Dana L; Youngblood, Robert W; Vedros, Kurt G

Optimal Bayesian supervised domain adaptation for RNA sequencing data

Journal Article · 2021 · Bioinformatics · OSTI ID:1853183

Boluki, Shahin; Qian, Xiaoning; Dougherty, Edward R.; +1 more

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

Citation Formats

References (22)

Similar Records

Related Subjects