An Overview, Challenges, and Future Directions - SAMSI

Experiments Models Connectivity Prediction Summary
Estimation and Prediction
Estimation is performed using MCMC methods (Gibbs)
Prediction:
For region g, we can write
Y g = (Y T g,1 , YT g,2 )T ∼ N ( (µ T g,1 , µT g,2 )T , Ψ g
)
, where Ψg = Σ g ⊗ I Vg .
Then E(Y i ∗ g,2|Y i ∗ g,1) = b i ∗ g , where
b i ∗ g = µ i ∗ g,2 + Ψ T g,12Ψ −1
g,11 (Y i ∗ g,1 − µ i ∗ g,1)
and µ i ∗ g = β g + φ g + 1 Vg ⊗ α i ∗ g + 1 Vg ⊗ X i ∗ gv γ gv .
Estimated conditional mean ˆb i ∗ g obtained from inputting the posterior
means of the corresponding parameters
The follow-up brain activity Y i ∗ g,2 is predicted using the estimated
conditional mean ˆb i ∗ g .
F. D. Bowman (Emory University) SAMSI: NDA RTP, NC 62 / 77