The Gaussian distribution used in the CAR specification above induces a high level of smoothness. In the same 1991 article, Besag et al. (1991) discussed an alternative specification using the heavier-tailed, double-exponential distribution rather than the Gaussian distribution in Equation 2. In effect, this is similar to performing a median-based local smoothing (or L1 norm) rather than a mean-based smoothing, thus allowing more abrupt changes in the geographical pattern of risk. We will refer to this model as L1-BYM.