Table 1 Bayesian spatiotemporal models considered for the evaluations
| Â | Poisson | Negative binomial | |
|---|---|---|---|
\(\mathrm{log}\left({r}_{i}\right)= {r}_{0}+{u}_{i}+{v}_{i}\) | \(\mathrm{log}\left({r}_{ij}\right)= {r}_{0}+{u}_{i}+{v}_{i}+{\beta }_{r}\bullet \mathrm{log}(\sum_{{\delta }_{i}}{y}_{{\delta }_{i},j-1})\) | ||
M1 \(\mathrm{log}\left({\mu }_{ij}\right)=\mathrm{log}\left({S}_{ij}\right)+{\alpha }_{0}+{\beta }_{ep1}\cdot \mathrm{log}\left({y}_{i,j-1}\right)\)Â Â | PM1 (Poisson likelihood with the mean model M1) | NBM1RS (Negative binomial likelihood with the mean model 1 and dispersion varied by area) | NBM1RST (Negative binomial likelihood with the mean model 1 and dispersion varied by area and time) |
M2 \(\mathrm{log}\left({\mu }_{ij}\right)=\mathrm{log}\left({S}_{ij}\right)+{\alpha }_{0}+{\beta }_{ep1}\cdot \mathrm{log}\left({y}_{i,j-1}\right)+{u}_{i}+{v}_{i}\)Â Â | PM2 | NBM2RS | NBM2RST |
M3 \(\mathrm{log}\left({\mu }_{ij}\right)=\mathrm{log}\left({S}_{ij}\right)+{\alpha }_{0}+{\beta }_{ep1}\cdot \mathrm{log}\left({y}_{i,j-1}\right)+{u}_{i}+{v}_{i}+{\beta }_{ep2}\cdot \mathrm{log}(\sum\limits_{{\delta }_{i}}{y}_{{\delta }_{i},j-1})\)Â Â | PM3 | NBM3RS | NBM3RST |