Bayesian model averaging
Definition
Bayesian model averaging is a statistical framework that combines inference across multiple competing models by weighting each model according to its posterior probability, rather than conditioning all conclusions on a single selected model. In the context of network psychometrics, it serves as the foundation for the inclusion Bayes factor, a quantity used to assess the evidence for or against conditional independence between pairs of variables in Markov Random Field models for ordinal and binary data. Applying this framework requires specifying prior distributions over both the network structure, meaning the configuration of present edges, and the edge weight parameters governing the strength of associations between connected variables. The scale of the prior distribution on partial correlations is particularly consequential, as even small variations can substantially alter how well the inclusion Bayes factor distinguishes between edge presence and absence across different sample sizes, numbers of variables, and network densities.
Sources: Sekulovski et al. (2024)
Related Terms
- network psychometrics (1 shared article)
- Bayes factor (1 shared article)
- Bayesian variable selection (1 shared article)
- Markov random fields (1 shared article)
- prior sensitivity (1 shared article)
Applications
Bayesian Model Averaging and Inclusion Bayes Factor
The inclusion Bayes factor is derived directly from Bayesian model averaging by averaging the likelihood of the data over all network structures in which a given edge is present, relative to all structures in which it is absent. This formulation means that the resulting test statistic inherits sensitivity to both the prior on the network structure and the prior on the edge weight parameters, a dependence that simulation work on ordinal Markov Random Field models has shown to be substantial.
Sources: Sekulovski et al. (2024)
Bayesian Model Averaging and Prior Distribution Sensitivity
Because Bayesian model averaging weights models by their posterior probabilities, the choice of prior distributions directly shapes the conclusions drawn about conditional independence. Simulation studies examining the ordinal Markov Random Field demonstrate that the scale parameter of the prior on edge weights is especially influential, with small changes producing large shifts in the inclusion Bayes factor's ability to distinguish present from absent edges under varying data conditions.
Sources: Sekulovski et al. (2024)
