%
%  WinBUGS 1.4 CODE FOR "DIRECT" METHOD, EXPONENTIAL KRIGING MODEL:
%
%    SB NOTE RE USE OF "USELESS":

% we need the
%    useless[i] <- x[i] + y[i]
% since the data includes the x and y coordinate vectors 
%       (WHICH ARE ONLY NEEDED FOR THE NONSPAIAL (IID) MODEL)
%
% These vectors are actually not needed in the code, which uses the
% inter-site distance matrix directly (also being fed in the data as matrix
% d). Basically, it is easier (and faster) to compute the inter-site
% distance matrix in R and then feed it directly to BUGS (as an object),
% rather than having BUGS compute it.

%%%%%%%%%%%%%%

model 

{

	for (i in 1:N) {
		Y[i] ~ dnorm(mu[i], error.prec)
		mu[i] <- inprod(X[i,],beta[]) + W[i]
		muW[i] <- 0.0
		useless[i] <- x[i]+y[i]
	}

	error.prec ~ dgamma(0.1,0.1)
	tausq <- 1/error.prec

	for (i in 1:p) {beta[i] ~ dnorm(0.0, 0.001)}

	W[1:N] ~ dmnorm(muW[], Omega[,])
	spat.prec ~ dgamma(0.1,0.1)
	sigmasq <- 1/spat.prec
	phi ~ dunif(0,10)	

	for (i in 1:N) {
		for (j in 1:N) {
			H[i,j] <- sigmasq*exp(-phi*d[i,j])
		}
	}

	Omega[1:N,1:N] <- inverse(H[,])	

}



#Initial Values

list(beta=c(0),phi=5.0,error.prec=1.0,spat.prec=1.0,W=c(0,0,0,0,0,0,0,0,0,0))



#Data: 
list(N=10, p=1,X = structure(.Data=c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1), .Dim = c(10, 1)), x=c(0.056,6.257,1.204,4.346,4.902,9.800,7.624,4.258,2.835,5.497),y=c(6.682,3.859,6.327,0.546,6.787,9.167,2.265,7.670,5.431,0.363),
Y=c(5.972,3.391,4.891,5.352,4.423,3.057,4.553,4.365,7.374,6.554), d = structure(.Data=c(0.0, 6.81334939658902, 
1.20163596817006, 7.48696173357391, 4.84713740263261, 10.0558819106034, 
8.76267727352776, 4.31658985774651, 3.04759610184814, 8.33871944605405, 
6.81334939658902, 0.0, 5.62350717968778, 3.82464246695034, 
3.2263305782266, 6.38182677608849, 2.09988690171638, 4.30345465875963, 
3.76580243772825, 3.57765509796571, 1.20163596817006, 5.62350717968778, 
0.0, 6.57967514395658, 3.72650023480477, 9.05300038661216, 
7.59712077039716, 3.33625014050206, 1.86090757427659, 7.34841105273787, 
7.48696173357391, 3.82464246695034, 6.57967514395658, 0.0, 
6.26571759657264, 10.2013605465154, 3.70138420053904, 7.12454349414754, 
5.11334978267671, 1.16545699191347, 4.84713740263261, 3.2263305782266, 
3.72650023480477, 6.26571759657264, 0.0, 5.44562246212497, 
5.27804585050187, 1.09289752493086, 2.47208919741987, 6.45149602805427, 
10.0558819106034, 6.38182677608849, 9.05300038661216, 10.2013605465154, 
5.44562246212497, 0.0, 7.23689021610802, 5.74062479178007, 
7.90372829745558, 9.7992971686749, 8.76267727352776, 2.09988690171638, 
7.59712077039716, 3.70138420053904, 5.27804585050187, 7.23689021610802, 
0.0, 6.36741556677432, 5.74091255812175, 2.85337221546717, 
4.31658985774651, 4.30345465875963, 3.33625014050206, 7.12454349414754, 
1.09289752493086, 5.74062479178007, 6.36741556677432, 0.0, 
2.65293233988355, 7.4113001558431, 3.04759610184814, 3.76580243772825, 
1.86090757427659, 5.11334978267671, 2.47208919741987, 7.90372829745558, 
5.74091255812175, 2.65293233988355, 0.0, 5.72458452640888, 
8.33871944605405, 3.57765509796571, 7.34841105273787, 1.16545699191347, 
6.45149602805427, 9.7992971686749, 2.85337221546717, 7.4113001558431, 
5.72458452640888, 0.0), .Dim = c(10, 10)))