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Efficient posterior probability mapping using Savage-Dickey ratios.

William D Penny1, Gerard R Ridgway

  • 1Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College, London, United Kingdom. w.penny@ucl.ac.uk

Plos One
|March 28, 2013
PubMed
Summary
This summary is machine-generated.

Statistical Parametric Mapping (SPM) is a common neuroimaging analysis method. A new Bayesian approach, Posterior Probability Mapping (PPM), offers advantages in interpreting brain activity and inactivity, with a computationally efficient Savage-Dickey-Taylor (SDT) method showing comparable accuracy to existing techniques.

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Area of Science:

  • Neuroimaging Analysis
  • Bayesian Statistics
  • Computational Neuroscience

Background:

  • Statistical Parametric Mapping (SPM) is the standard for mass-univariate neuroimaging analysis.
  • Posterior Probability Mapping (PPM) offers a Bayesian alternative with advantages in effect size inference and declaring regions inactive.
  • Current PPM model comparisons use the computationally intensive Independent Model Optimization (IMO) procedure.

Purpose of the Study:

  • To introduce a computationally efficient Bayesian model comparison method for neuroimaging data.
  • To validate the accuracy and performance of the proposed Savage-Dickey-Taylor (SDT) method.
  • To compare SDT with the existing Independent Model Optimization (IMO) procedure.

Main Methods:

  • Development of the Savage-Dickey-Taylor (SDT) method using Savage-Dickey approximations for Bayes factors and Taylor-series approximations for posterior covariance matrices.
  • Simulations to assess the accuracy of the SDT method.
  • Application of SDT to functional magnetic resonance imaging (fMRI) data for both first-level and second-level models.

Main Results:

  • The Savage-Dickey-Taylor (SDT) method demonstrates accuracy comparable to the Independent Model Optimization (IMO) procedure in simulations.
  • Excellent agreement between SDT and IMO was observed for second-level fMRI models.
  • Reasonable agreement was found between SDT and IMO for first-level fMRI models, highlighting SDT's efficiency.

Conclusions:

  • The Savage-Dickey-Taylor (SDT) method provides a computationally efficient alternative for Bayesian model comparison in neuroimaging.
  • SDT offers a Bayesian analogue to classical SPM-F tests, enabling interactive model comparison.
  • This approach enhances the interpretability of neuroimaging results by allowing precise inferences on effect sizes and region inactivity.