(1) 
(2) 
(3) 
1.  is positive definite,

2.  any positive definite matrix is the matrix exponential of some matrix,

3.  ,

4.  . 
(4) 
Variables  SAR Model  MESS Model 
ln(Land Area)  0.0152  0.0188 
Deviance  1142.64  1394.59 
ln(Population)  0.0189  0.0233 
Deviance  132.87  177.70 
ln(Per Capita Income)  0.4613  0.4786 
Deviance  31229.72  23987.24 
ln(Age)  0.0685  0.0689 
Deviance  1213.15  1097.93 
Intercept  1.6861  1.3492 
Deviance  3464.33  1945.65 
Time (in seconds) Matlab  2414.92  3.36 
Time (in seconds) FORTRAN 90  —  0.536 
57,647  57,647  
5  5 