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Bayesian Case-deletion Model Complexity and Information Criterion.

Hongtu Zhu1, Joseph G Ibrahim2, Qingxia Chen3

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Summary
This summary is machine-generated.

We link Bayesian influence measures to predictive performance, introducing Bayesian case-deletion model complexity (BCMC) to quantify model parameters. This leads to a new Bayesian case-deletion information criterion (BCIC) for model comparison.

Keywords:
BayesianCase influence measuresCross ValidationInformation criterionMarkov chain Monte CarloModel complexity

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Bayesian Inference

Background:

  • Assessing individual observation influence is crucial in Bayesian analysis.
  • Evaluating and comparing statistical models relies on predictive performance metrics.

Purpose of the Study:

  • To connect Bayesian case influence measures with Bayesian predictive methods.
  • To propose novel Bayesian case-deletion model complexity (BCMC) measures.
  • To develop a Bayesian case-deletion information criterion (BCIC) for model comparison.

Main Methods:

  • Establishing a formal link between case influence and predictive performance.
  • Developing and exploring properties of BCMC in linear models.
  • Constructing BCIC by integrating BCMC with conditional deviance.
  • Investigating BCIC properties and its relation to existing criteria like DIC.

Main Results:

  • A novel connection between Bayesian case influence and predictive model evaluation is established.
  • New Bayesian case-deletion model complexity (BCMC) measures are proposed.
  • A new Bayesian case-deletion information criterion (BCIC) is developed for model comparison.

Conclusions:

  • The proposed BCMC and BCIC offer a new framework for Bayesian model assessment and comparison.
  • The methodology is validated through simulations and a real-world example using linear mixed models.