Table 1.

Bayesian spatiotemporal models considered for the evaluations

	Poisson	Negative binomial
		$\log \left(r_i\right)=r_0+u_i+v_i$	$\log \left(r_{\mathit{ij}}\right)=r_0+u_i+v_i+{\beta }_r\bullet \log ({\sum }_{{\delta }_i}{y}_{{\delta }_i,j-1})$
M1 $\log \left({\mu }_{\mathit{ij}}\right)=\log \left(S_{\mathit{ij}}\right)+{\alpha }_0+{\beta }_{ep1}·\log \left(y_{i,j-1}\right)$	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 $\log \left({\mu }_{\mathit{ij}}\right)=\log \left(S_{\mathit{ij}}\right)+{\alpha }_0+{\beta }_{ep1}·\log \left(y_{i,j-1}\right)+u_i+v_i$	PM2	NBM2RS	NBM2RST
M3 $\log \left({\mu }_{\mathit{ij}}\right)=\log \left(S_{\mathit{ij}}\right)+{\alpha }_0+{\beta }_{ep1}·\log \left(y_{i,j-1}\right)+u_i+v_i+{\beta }_{ep2}·\log (\sum _{{\delta }_i}{y}_{{\delta }_i,j-1})$	PM3	NBM3RS	NBM3RST