An Overview, Challenges, and Future Directions - SAMSI

Experiments Models Connectivity Prediction Summary
Model
Y ig (v)|β g , φ g , α ig , γ gv , Ω g ∼ N(β g (v) + φ g (v) + α ig + X ig γ g , Ω g )
φ g (v)|φ g (v ′ ), v ≠ v ′ , ρ, Σ ∼ N ( ρ ∑ w vv ′
w v+
φ g (v ′ 1
),
w v+
Σ ) ( MCAR(ρ, Σ) )
β gj (v)|λ 2 gj ∼ N(β 0gj , λ 2 gj) (λ vgj = λ gj , ∀v ∈ region g)
Ω −1
g ∼ Wishart ( (c 1 Z 1 ) −1 )
, c 1
Σ −1 ∼ Wishart ( (c 2 Z 2 ) −1 , c 2
)
α ij |Γ j ∼ N(0, Γ j )
(α ij = α (j)
i
Γ −1
j
∼ Wishart((h j H j ) −1 , h j ) j = 1, 2
λ −2
gj
∼ Gamma(a j , b j )
γ gjq |τ 2 gjq ∼ N(0, τ 2 gjq)
τ −2
gjq ∼ Gamma(e 0, f 0 )
= (α (j)
i1 , . . . , α(j) iG )′ )
q = 1, . . . , Q (covariates)
F. D. Bowman (Emory University) SAMSI: NDA RTP, NC 61 / 77