2022
DOI: 10.1007/s11336-022-09848-8
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Objective Bayesian Edge Screening and Structure Selection for Ising Networks

Abstract: The Ising model is one of the most widely analyzed graphical models in network psychometrics. However, popular approaches to parameter estimation and structure selection for the Ising model cannot naturally express uncertainty about the estimated parameters or selected structures. To address this issue, this paper offers an objective Bayesian approach to parameter estimation and structure selection for the Ising model. Our methods build on a continuous spike-and-slab approach. We show that our methods consiste… Show more

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Cited by 19 publications
(17 citation statements)
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“…The term on the right is the posterior odds, which indicates the relative plausibility of the rival models after having seen the data. In this paper, we assume that the prior odds are equal to one by assuming p(S s ) = p(S t ), which makes the Bayes factor equal to the posterior odds (see Marsman, Huth, Waldorp, & Ntzoufras, 2022, for a different approach). The subscripts in the Bayes factor notation indicate in which direction the support is expressed.…”
Section: Bayesian Hypothesis Testing: the Bayes Factormentioning
confidence: 99%
“…The term on the right is the posterior odds, which indicates the relative plausibility of the rival models after having seen the data. In this paper, we assume that the prior odds are equal to one by assuming p(S s ) = p(S t ), which makes the Bayes factor equal to the posterior odds (see Marsman, Huth, Waldorp, & Ntzoufras, 2022, for a different approach). The subscripts in the Bayes factor notation indicate in which direction the support is expressed.…”
Section: Bayesian Hypothesis Testing: the Bayes Factormentioning
confidence: 99%
“…Several papers in the special issue aim to fill that gap. For example, Marsman et al (2022; this issue) offer Bayesian solutions for assessing edge inclusion for the Ising model, a network for binary variables, addressing similar questions as Williams and Mulder (2020a) did for GGMs. While Epskamp et al (2022, this issue) offer a classical approach to gauge the heterogeneity of a GGM applied to independent datasets, Lee, Chen, DeSarbo, and Xue (2022; this issue) gauge the heterogeneity of networks of ordinal variables estimated from cross-sectional data.…”
Section: How Can We Conduct Confirmatory Tests Of the Relationship Be...mentioning
confidence: 99%
“…Altogether this paper pointed to the necessity of solid uncertainty quantification in complex statistical models, such as networks, to not draw unwarranted inferential conclusions. Bayesian approaches offer an avenue to address this issue by allowing to quantify structure uncertainty, determine parameter stability, obtain edge inclusion evidence and acknowledging structure uncertainty in further inferential decision through Bayesian model-averaging (Marsman et al, 2022;Williams et al, 2021).…”
Section: Limitationsmentioning
confidence: 99%