scholarly journals Bayesian hypothesis testing for Gaussian graphical models: Conditional independence and order constraints

2020 ◽  
Vol 99 ◽  
pp. 102441 ◽  
Author(s):  
Donald R. Williams ◽  
Joris Mulder
Keyword(s):  
Hypothesis Testing ◽  
Graphical Models ◽  
Conditional Independence ◽  
Gaussian Graphical Models ◽  
Bayesian Hypothesis Testing ◽  
Order Constraints

scholarly journals BGGM: A R Package for Bayesian Gaussian Graphical Models

2019 ◽  
Author(s):  
Donald Ray Williams ◽  
Joris Mulder
Keyword(s):  
Hypothesis Testing ◽  
Graphical Models ◽  
Bayes Factor ◽  
R Package ◽  
Predictive Distribution ◽  
Gaussian Graphical Models ◽  
Posterior Predictive Distribution ◽  
Bayesian Approaches ◽  
Bayesian Hypothesis Testing ◽  
Partial Correlations

Gaussian graphical models (GGM) allow for learning conditional independence structures that are encoded by partial correlations. Whereas there are several \proglang{R} packages for classical (i.e., frequentist) methods, there are only two that implement a Bayesian approach. These are exclusively focused on identifying the graphical structure; that is, detecting non-zero effects. The \proglang{R} package \pkg{BGGM} not only fills this gap, but it also includes novel Bayesian methodology for extending inference beyond identifying non-zero relations. \pkg{BGGM} is built around two Bayesian approaches for inference--estimation and hypothesis testing. The former focuses on the posterior distribution and includes extensions to assess predictability, as well as methodology to compare partial correlations. The latter includes methods for Bayesian hypothesis testing, in both exploratory and confirmatory contexts, with the novel matrix-$F$ prior distribution. This allows for testing order and equality constrained hypotheses, as well as a combination of both with the Bayes factor. Further, there are two approaches for comparing any number of GGMs with either the posterior predictive distribution or Bayesian hypothesis testing. This work describes the software implementation of these methods. We end by discussing future directions for \pkg{BGGM}.

scholarly journals Comparing Gaussian Graphical Models with the Posterior Predictive Distribution and Bayesian Model Selection

2019 ◽  
Author(s):  
Donald Ray Williams ◽  
Philippe Rast ◽  
Luis Pericchi ◽  
Joris Mulder
Keyword(s):  
Model Selection ◽  
Hypothesis Testing ◽  
Graphical Models ◽  
Bayesian Model ◽  
Bayesian Model Selection ◽  
Predictive Distribution ◽  
Network Structures ◽  
Gaussian Graphical Models ◽  
Posterior Predictive Distribution ◽  
Leibler Divergence

Gaussian graphical models are commonly used to characterize conditional independence structures (i.e., networks) of psychological constructs. Recently attention has shifted from estimating single networks to those from various sub-populations. The focus is primarily to detect differences or demonstrate replicability. We introduce two novel Bayesian methods for comparing networks that explicitly address these aims. The first is based on the posterior predictive distribution, with Kullback-Leibler divergence as the discrepancy measure, that tests differences between two multivariate normal distributions. The second approach makes use of Bayesian model selection, with the Bayes factor, and allows for gaining evidence for invariant network structures. This overcomes limitations of current approaches in the literature that use classical hypothesis testing, where it is only possible to determine whether groups are significantly different from each other. With simulation we show the posterior predictive method is approximately calibrated under the null hypothesis ($\alpha = 0.05$) and has more power to detect differences than alternative approaches. We then examine the necessary sample sizes for detecting invariant network structures with Bayesian hypothesis testing, in addition to how this is influenced by the choice of prior distribution. The methods are applied to post-traumatic stress disorder symptoms that were measured in four groups. We end by summarizing our major contribution, that is proposing two novel methods for comparing GGMs, which extends beyond the social-behavioral sciences. The methods have been implemented in the R package BGGM.

scholarly journals On Formalizing Theoretical Expectations: Bayesian Testing of Central Structures in Psychological Networks

2020 ◽  
Author(s):  
Josue E. Rodriguez ◽  
Donald Ray Williams ◽  
Philippe Rast ◽  
Joris Mulder
Keyword(s):  
Hypothesis Testing ◽  
Graphical Models ◽  
Network Theory ◽  
Dependence Structure ◽  
Gaussian Graphical Models ◽  
Psychological Constructs ◽  
Partial Correlations ◽  
Psychopathology Symptom ◽  
The Rich ◽  
Cohesive Framework

Network theory has emerged as a popular framework for conceptualizing psychological constructs and mental disorders. Initially, network analysis was motivated in part by the thought that it can be used for hypothesis generation. Although the customary approach for network modeling is inherently exploratory, we argue that there is untapped potential for confirmatory hypothesis testing. In this work, we bring to fruition the potential of Gaussian graphical models for generating testable hypotheses. This is accomplished by merging exploratory and confirmatory analyses into a cohesive framework built around Bayesian hypothesis testing of partial correlations. We first present a motivating example based on a customary, exploratory analysis, where it is made clear how information encoded by the conditional (in)dependence structure can be used to formulate hypotheses. Building upon this foundation, we then provide several empirical examples that unify exploratory and confirmatory testing in psychopathology symptom networks. In particular, we (1) estimate exploratory graphs; (2) derive hypotheses based on the most central structures; and (3) test those hypotheses in a confirmatory setting. Our confirmatory results uncovered an intricate web of relations, including an order to edge weights within comorbidity networks. This illuminates the rich and informative inferences that can be drawn with the proposed approach. We conclude with recommendations for applied researchers, in addition to discussing how our methodology answers recent calls to begin developing formal models related to the conditional (in)dependence structure of psychological networks.

scholarly journals BGGM: Bayesian Gaussian Graphical Models in R

2020 ◽  
Author(s):  
Donald Ray Williams ◽  
Joris Mulder
Keyword(s):  
Bayesian Inference ◽  
Hypothesis Testing ◽  
Graphical Models ◽  
Model Comparison ◽  
Bayes Factor ◽  
R Package ◽  
Predictive Distribution ◽  
Gaussian Graphical Models ◽  
Posterior Predictive Distribution

The R package BGGM provides tools for making Bayesian inference in Gaussian graphicalmodels (GGM). The methods are organized around two general approaches for Bayesian inference: (1) estimation and (2) hypothesis testing. The key distinction is that the formerfocuses on either the posterior or posterior predictive distribution (Gelman, Meng, & Stern,1996; see section 5 in Rubin, 1984), whereas the latter focuses on model comparison withthe Bayes factor (Jeffreys, 1961; Kass & Raftery, 1995).

scholarly journals Bayesian Hypothesis Testing for Gaussian Graphical Models:Conditional Independence and Order Constraints

2019 ◽  
Author(s):  
Donald Ray Williams ◽  
Joris Mulder
Keyword(s):  
Graphical Models ◽  
Partial Correlation ◽  
R Package ◽  
The Novel ◽  
Gaussian Graphical Models ◽  
Conditional Dependence ◽  
Correlation Networks ◽  
The Social ◽  
Partial Correlations ◽  
Order Constraints

Gaussian graphical models (GGM; partial correlation networks) have become increasingly popular in the social and behavioral sciences for studying conditional (in)dependencies between variables. In this work, we introduce exploratory and confirmatory Bayesian tests for partial correlations. For the former, we first extend the customary GGM formulation that focuses on conditional dependence to also consider the null hypothesis of conditional independence for each partial correlation. Here a novel testing strategy is introduced that can provide evidence for a null, negative, or positive effect. We then introduce a test for hypotheses with order constraints on partial correlations. This allows for testing theoretical and clinical expectations in GGMs. The novel matrix$-F$ prior distribution is described that provides increased flexibility in specification compared to the Wishart prior. The methods are applied to PTSD symptoms. In several applications, we demonstrate how the exploratory and confirmatory approaches can work in tandem: hypotheses are formulated from an initial analysis and then tested in an independent dataset. The methodology is implemented in the R package BGGM.

scholarly journals Fast Bayesian inference in large Gaussian graphical models

Biometrics ◽  
2019 ◽  
Vol 75 (4) ◽  
pp. 1288-1298
Author(s):  
Gwenaël G. R. Leday ◽  
Sylvia Richardson
Keyword(s):  
Bayesian Inference ◽  
Graphical Models ◽  
Gaussian Graphical Models

scholarly journals Gaussian graphical modeling of the serum exposome and metabolome reveals interactions between environmental chemicals and endogenous metabolites

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Vincent Bessonneau ◽  
Roy R. Gerona ◽  
Jessica Trowbridge ◽  
Rachel Grashow ◽  
Thomas Lin ◽  
...  
Keyword(s):  
Graphical Models ◽  
Association Studies ◽  
Environmental Chemicals ◽  
Gaussian Graphical Models ◽  
Metabolomics Data ◽  
Health And Nutrition ◽  
Novel Approach ◽  
Disease Causation ◽  
Women Firefighters ◽  
Endogenous Metabolites

AbstractGiven the complex exposures from both exogenous and endogenous sources that an individual experiences during life, exposome-wide association studies that interrogate levels of small molecules in biospecimens have been proposed for discovering causes of chronic diseases. We conducted a study to explore associations between environmental chemicals and endogenous molecules using Gaussian graphical models (GGMs) of non-targeted metabolomics data measured in a cohort of California women firefighters and office workers. GGMs revealed many exposure-metabolite associations, including that exposures to mono-hydroxyisononyl phthalate, ethyl paraben and 4-ethylbenzoic acid were associated with metabolites involved in steroid hormone biosynthesis, and perfluoroalkyl substances were linked to bile acids—hormones that regulate cholesterol and glucose metabolism—and inflammatory signaling molecules. Some hypotheses generated from these findings were confirmed by analysis of data from the National Health and Nutrition Examination Survey. Taken together, our findings demonstrate a novel approach to discovering associations between chemical exposures and biological processes of potential relevance for disease causation.

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