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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Post hoc Bayesian model selection.

Karl Friston1, Will Penny

  • 1The Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London, UK. k.friston@fil.ion.ucl.ac.uk

Neuroimage
|April 5, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a Bayesian method for post hoc model selection and optimization. It efficiently scores many models using a single full model inversion, aiding in Bayesian inference and model comparison.

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Model Selection

Background:

  • Post hoc model selection is crucial for refining statistical models.
  • Existing methods can be computationally intensive for large numbers of models.
  • Bayesian approaches offer a principled framework for model comparison.

Purpose of the Study:

  • To develop an efficient Bayesian procedure for post hoc model selection and optimization.
  • To provide a method for scoring reduced models based on a full model's posterior density.
  • To enable selection among discrete and continuous model spaces.

Main Methods:

  • A Bayesian model selection scheme using priors on parameters.
  • Scoring models via the posterior density of the full model.
  • Utilizing shrinkage priors to remove parameters for discrete model selection.
  • Optimizing continuous model spaces via hyperparameter tuning.
  • Employing Laplace approximation for simplified evidence calculations.

Main Results:

  • The proposed scheme efficiently scores numerous models after a single full model inversion.
  • It facilitates selection between discrete models by effectively removing parameters.
  • The method allows for optimization within continuous model spaces.
  • Simplified expressions for model evidence are derived using Laplace approximation.
  • Special cases include Savage-Dickey tests and automatic relevance determination.

Conclusions:

  • The described Bayesian procedure offers an efficient and flexible approach to post hoc model selection and optimization.
  • It unifies discrete and continuous model space exploration.
  • The method simplifies evidence calculation, particularly under Gaussian approximations.
  • Applicable to various models, including linear and nonlinear state-space models.