\(\Pr \left( {m_{ij} } \right) = \left( {e^{ - \mu ij} \mu_{ij}^{{m_{ij} }} } \right)/\left( {m_{ij} !} \right)\)
Moran Eigenvector network filtering in Poisson regression \citet{Chun_2008,Chun_2011,Chun_2013,Griffith_2011}
Spatial filtering methods have been applied to account for spatial autocorrelation by focusing on isolating spatial effects in the standard linear regression model . The decomposition of spatial observations provides the conceptual background for spatial filtering \cite{Haining_2003} . Spatially distributed observations can be decomposed into a systematic trend and an autocorrelated unexplained random component. The autocorrelated unexplained random component can be divided further into a stochastic spatial signal and an independent white noise component. In the regression context, a systematic trend can be explained by a set of exogenous variables. Assuming underlying spatial autocorrelation, then the residuals are composed of a stochastic spatial signal and white noise. Spatial filtering enforces independence by isolating the stochastic spatial signal from the white noise component with proxy variables having an underlying spatial pattern. Once the stochastic signal has been successfully identified, a regression model can be calibrated for spatially distributed observations without suffering from the ramifications of spatial autocorrelation by using standard techniques that rely on stochastic independence among the observations.