\(y\left(s_{i},\ t\right)\ \sim\ Bernoulli(p\left(s_{i},\ t\right))\) (1)
\(\log\left(\frac{p\left(s_{i},\ t\right)\ }{1-\ p\left(s_{i},\ t\right)\text{\ \ }}\right)=X\left(s_{i},\ t\right)\beta+z\left(s_{i},\ t\right)\) (2)
\(z\left(s_{i},t\right)\ \sim\ \phi z\left(s_{i},\ t-1\right)+\ \omega\left(s_{i},\ t\right),\ t=2,\ 3,\ldots\) (3)
\(\omega\left(s,t\right)\ \sim\ N(0,\ \sum\left(s,\rho,\sigma^{2}\right))\) (4)
\(z\left(s,1\right)\ \sim\ N(0,\ \sum\frac{\left(s,\rho,\sigma^{2}\right)}{(1-\phi^{2}})\)) (5)
\(\log\rho\ \sim\ N(a_{\rho},\ b_{\rho}^{2})\) (6)
\(\log\frac{e^{\phi}+1}{e^{\phi}-1}\sim\ N(a_{\phi},\ b_{\phi}^{2})\) (7)
\(\log\sigma\ \sim\ N(a_{\sigma},\ b_{\sigma}^{2})\) (8)
\(\beta\ \sim\ N(0,\ s)\) (9)