Table 1.

Priors for unknown parameters

Parameter	Distribution type	Formula
N	Uniform	$P(N\mid \mathbf{m})=\frac{1}{N_{max}-N_{min}+1},N\in [N_{min},N_{max}]$
Θ	Uniform	$P(\mathit{\Theta }\mid N,\mathbf{X},\mathbf{m})={(\frac{1}{2\pi })}^N,\mathit{\Theta }\in [0,2\pi ]$
J	Gaussian	$P(\mathbf{J}\mid N,\mathbf{m})=\frac{1}{{\prod }_{i=1}^N\left[{(2\pi {\sigma }_i^2)}^{T/2}{\mid \overline{\mathbf{C}}\mid }^{1/2}\right]}exp\left(-\frac{1}{2}\sum \frac{1}{{\sigma }_i^2}{J}_i^{\prime }{\overline{\mathbf{C}}}^{-1}{J}_i\right)$
C	k-th order Inverse Wishart	$P(\mathbf{C}\mid \mathbf{m})=\frac{1}{Z_c}{\mid {LT\mathbf{C}}_0\mid }^{(k-LT-1)/2}{\mid \mathbf{C}\mid }^{-k/2}exp(-\frac{1}{2}Tr({LT\mathbf{C}}_0{\mathbf{C}}^{-1}))$
X	Exponential	$P(\mathbf{X}\mid \mathbf{fMRI},N,\mathbf{m})=\frac{1}{Z_x^N}exp(-\frac{1}{2}\alpha p_{\text{x}}^{-\eta }N)$