scholarly journals Comparing Gaussian graphical models with the posterior predictive distribution and Bayesian model selection.

2020 ◽  
Vol 25 (5) ◽  
pp. 653-672 ◽  
Author(s):  
Donald R. Williams ◽  
Philippe Rast ◽  
Luis R. Pericchi ◽  
Joris Mulder
Keyword(s):  
Model Selection ◽  
Graphical Models ◽  
Bayesian Model ◽  
Bayesian Model Selection ◽  
Predictive Distribution ◽  
Gaussian Graphical Models ◽  
Posterior Predictive Distribution

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 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 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 Bayesian model selection on scalar ε -field dark energy

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
J. Alberto Vázquez ◽  
David Tamayo ◽  
Anjan A. Sen ◽  
Israel Quiros
Keyword(s):  
Dark Energy ◽  
Model Selection ◽  
Bayesian Model ◽  
Bayesian Model Selection

scholarly journals Accounting for cell lineage and sex effects in the identification of cell-specific DNA methylation using a Bayesian model selection algorithm

PLoS ONE ◽  
2017 ◽  
Vol 12 (9) ◽  
pp. e0182455 ◽  
Author(s):  
Nicole White ◽  
Miles Benton ◽  
Daniel Kennedy ◽  
Andrew Fox ◽  
Lyn Griffiths ◽  
...  
Keyword(s):  
Dna Methylation ◽  
Model Selection ◽  
Bayesian Model ◽  
Cell Lineage ◽  
Bayesian Model Selection ◽  
Selection Algorithm ◽  
Sex Effects
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