TABLE II.

Notations for variables and parameters used in the model for a given parcel with J_γ voxels.

	Notation	Definition	Dimension
Variables	y j ∈ ℝN	Observed BOLD signal at voxel j	N
	b j ∈ ℝN	Acquisition noise vector at voxel j	N
	h γ = {hd Δ t, d = 0 … D} ∈ ℝD +1	HRF sampled at Δt	D + 1
	$a_j^m\in ℝ$	NRL at voxel j for condition m	1
	${\mathit{a}}^m=\{a_j^m,j\in {\mathcal{P}}_{\gamma }\}\in {ℝ}^{J_{\gamma }}$n	NRLs for condition m	Jγ
	$q_j^m\in \{0,1\}$	Activation class for voxel j and condition m	1
	${\mathit{q}}^m=\{q_j^m,j\in {\mathcal{P}}_{\gamma }\}\in {\{0,1\}}^{J_{\gamma }}$	Activation classes for condition m	Jγ
Unknown Parameters	ℓ j ∈ ℝO	Low frequency drifts for voxel j	O
	Γ j ∈ ℝN × N	Noise precision matrix for voxel j	N × N
	μ m = {μ 0 m, μ 1 m} ∈ ℝ2	Mixture model means for NRLs in condition m	2
	${\mathit{v}}_m=\{v_{0m},v_{1m}\}\in {ℝ}_{+}^2$	Mixture model variances for NRLs in condition m	2
	βm ∈ ℝ+	Potts regularization parameter for condition m	1
	v h ∈ ℝ+	HRF prior parameter	1
Fixed	X m ∈ {0, 1}N × D +1	Binary stimulus occurrence matrix for condition m	N × (D + 1)
	P ∈ ℝN × O	Low frequency orthonormal function basis	N × O