Bayesian variable selection
Definition
Bayesian variable selection refers to the use of prior distributions over model structures and parameters to determine which variables or connections should be included in a statistical model, evaluated through Bayes factors rather than frequentist significance thresholds. In network psychometrics, this approach is applied to Markov Random Field models for binary and ordinal data, where the selection problem concerns which edges between psychological variables, such as symptoms of major depressive disorder or generalized anxiety disorder, are present in the network. The inclusion Bayes factor, derived from Bayesian model averaging, quantifies evidence for or against each edge, thereby distinguishing between the absence of evidence and the evidence of absence for a conditional relationship. A defining feature of this framework is the requirement to specify two sets of prior distributions: one over the network structure and one over the edge weight parameters, with the structure prior governing which parameters receive a non-zero prior in the first place. The scale of the prior on edge weight parameters has been shown to substantially affect the inclusion Bayes factor's sensitivity, meaning that prior specification is not merely a formal requirement but directly shapes inferential conclusions about conditional independence.
Sources: Sekulovski et al. (2024)
Related Terms
- network psychometrics (1 shared article)
- Bayes factor (1 shared article)
- Bayesian model averaging (1 shared article)
- Markov random fields (1 shared article)
- prior sensitivity (1 shared article)
Applications
Bayesian Variable Selection and Conditional Independence Testing
Bayesian variable selection in graphical models is operationalized through conditional independence testing, where the goal is to determine whether pairs of variables retain a direct association after accounting for all remaining variables in the network. The inclusion Bayes factor quantifies this evidence by averaging across network structures, and simulation studies examining ordinal and binary Markov Random Field models show that the choice of prior scale substantially alters how well the Bayes factor separates present from absent edges.
Sources: Sekulovski et al. (2024)
Bayesian Variable Selection and Prior Sensitivity Analysis
The reliability of Bayesian variable selection depends on how sensitive the inclusion Bayes factor is to the choice of prior distributions on both the network structure and the edge weight parameters. Simulation work on ordinal Markov Random Field models demonstrates that even small variations in the prior scale can produce meaningfully different Bayes factor values across conditions defined by sample size, number of variables, and network density.
Sources: Sekulovski et al. (2024)
