Tan, LSL;
Jasra, A;
De Iorio, M;
Ebbels, TMD;
(2017)
Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks.
The Annals of Applied Statistics
, 11
(4)
pp. 2222-2251.
10.1214/17-AOAS1076.
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Abstract
We investigate the effect of cadmium (a toxic environmental pollutant) on the correlation structure of a number of urinary metabolites using Gaussian graphical models (GGMs). The inferred metabolic associations can provide important information on the physiological state of a metabolic system and insights on complex metabolic relationships. Using the fitted GGMs, we construct differential networks, which highlight significant changes in metabolite interactions under different experimental conditions. The analysis of such metabolic association networks can reveal differences in the underlying biological reactions caused by cadmium exposure. We consider Bayesian inference and propose using the multiplicative (or Chung–Lu random graph) model as a prior on the graphical space. In the multiplicative model, each edge is chosen independently with probability equal to the product of the connectivities of the end nodes. This class of prior is parsimonious yet highly flexible; it can be used to encourage sparsity or graphs with a pre-specified degree distribution when such prior knowledge is available. We extend the multiplicative model to multiple GGMs linking the probability of edge inclusion through logistic regression and demonstrate how this leads to joint inference for multiple GGMs. A sequential Monte Carlo (SMC) algorithm is developed for estimating the posterior distribution of the graphs.
| Type: | Article |
|---|---|
| Title: | Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/17-AOAS1076 |
| Publisher version: | http://doi.org/10.1214/17-AOAS1076 |
| Language: | English |
| Additional information: | © Institute of Mathematical Statistics, 2017. This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Statistics & Probability, Mathematics, Gaussian graphical models, prior specification, multiplicative model, sequential Monte Carlo, SEQUENTIAL MONTE-CARLO, INVERSE COVARIANCE ESTIMATION, COLLABORATION NETWORKS, GENE-EXPRESSION, SELECTION, PATHWAYS, LASSO |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10042044 |
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