What question did this study set out to answer?

To develop straightforward methods for constructing parameter priors and computing marginal likelihoods for model selection among directed acyclic graphical (DAG) models.

May 5, 2021Open Access

Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions

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To develop straightforward methods for constructing parameter priors and computing marginal likelihoods for model selection among directed acyclic graphical (DAG) models.
Formulated assumptions to derive parameter priors across multiple DAG models using a minimal set of prior assessments.
Devised an approach to directly calculate marginal likelihoods for complete observational data samples.
Applied the framework to Gaussian DAG models consisting of recursive linear regressions and derived distribution characterizations.
Proved that the normal-Wishart distribution is the uniquely valid parameter prior satisfying the specified assumptions for complete Gaussian DAG models.
Characterized the Wishart distribution for positive-definite symmetric matrices based on block partitioning independence conditions.
Established related mathematical characterizations for normal and normal-Wishart probability distributions.

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Implication

Theoretical analysis establishes parameter priors and marginal likelihood computations for graphical models, characterizing the Wishart distribution.

Cite This Study

Geiger et al. (2021) studied this question.

synapsesocial.com/papers/6a0fabb692676d5461fcf2e9 https://doi.org/10.48550/arxiv.2105.03248

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Implication

Theoretical analysis establishes parameter priors and marginal likelihood computations for graphical models, characterizing the Wishart distribution.

Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions

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Discussion

Implication

Cite This Study

Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions

Key Points

Discussion

Implication

Cite This Study

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