1 / 24

Bayesian Model Reduction for Group Studies

This paper explores the commonalities and differences in effective connectivity within and between groups using Bayesian model reduction. It investigates the predictive power of different connections and group differences on connectivity.

jamesgmiller
Download Presentation

Bayesian Model Reduction for Group Studies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bayesian Model Reduction for Group Studies Peter Zeidman

  2. Background

  3. Questions • What are the commonalities in effective connectivity across subjects within a group? • What are the differences in effective connectivity between groups? • Which combination of connections best predicts a group difference (or covariate)? • Which combination of group differences (or covariates) are most predictive of the connectivity?

  4. Inference over models Random effects Bayesian Model Selection (RFX BMS) SPM estimates a hierarchical model with variables: Outputs: Expected probability of model 2 Exceedance probability of model 2 Stephan et al. 2009, NeuroImage

  5. Inference over parameters Bayesian Model Selection: RFX 0.35 0.3 SPM calculates a weighted average of the parameters over models: 0.25 0.2 Model Expected Probability 0.15 0.1 0.05 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Region 1 to 2 Models To give a posterior distribution for each connection:

  6. Hierarchical model of parameters Parametric Empirical Bayes DCM for subject i Second level (linear) model Priors on second level parameters

  7. Hierarchical model of parameters Design matrix (covariates) Matrix of DCM connections (1) Ä Between-subjects (X) Within-subjects (W) X K 1 1 5 2 2 10 3 3 Connection Connection 15 Subject 4 4 20 5 5 25 6 6 30 1 2 3 2 4 6 5 10 15 Covariate Connection PEB Parameter

  8. Hierarchical model of parameters Second level precision Second level (PEB) parameter Second level (PEB) parameter

  9. Hierarchical model of parameters Second level parameter(s) Second level precision(s) First level DCM parameter

  10. Bayesian Model Reduction Full model Model inversion (VB) Priors: Nested / reduced model X Bayesian Model Reduction (BMR) Priors:

  11. PEB Estimation First level Second level DCMs Subject 1 . PEB Estimation . Subject N First level free energy / parameters with empirical priors

  12. Software implementation

  13. GCM_XX.mat Full model models subjects sessions = DCM

  14. GCM_XX.mat Full model models subjects = DCM

  15. Overview • Estimate first level models, optionally re-starting using PEBGCM_XX.mat • Estimate second level PEB model, optionally with multiple covariatesPEB_XX.mat • Compare combinations of parameters of the PEB modelBMA_XX.mat

  16. BMR estimation models spm_dcm_fit subjects

  17. BMR estimation models spm_dcm_bmr subjects

  18. BMR + PEB estimation models models models spm_dcm_fit spm_dcm_bmr subjects spm_dcm_peb Repeat PEBs Models with empirical priors

  19. 1 0.8 0.6 0.4 0.2 0 1 2 3 4 GCM_XX.mat models spm_dcm_bmc spm_dcm_bma subjects BMA

  20. GCM_XX.mat models spm_dcm_peb subjects PEB

  21. spm_dcm_peb PEB_XX.mat Covariate 1 Mean Covariate 2 1 2 3 DCM Connection 4 5 6 5 10 15 PEB Parameter

  22. Summary • Estimate first level models, optionally re-starting using PEBGCM_XX.mat • Estimate second level PEB model, optionally with multiple covariatesPEB_XX.mat • Compare combinations of parameters of the PEB modelBMA_XX.mat

  23. Demo

  24. Generative model FORWARDMODULATORY INPUT (B) GROUP 1: N(0.3, 0.06) GROUP 2: N(0.7, 0.06) R1 R2 DRIVING (C) Model comparison ✔ Model 1 Model 2 R1 R2 R1 R2 R1 R2 R1 R2 Model 3 Model 4

More Related