Oi	~	Poisson(mi)
	log mi	=	log Ei + a0 + a1xi / 10 +  bi



model {

	# Likelihood
	for (i in 1 : N) {
		O[i]  ~ dpois(mu[i])
		log(mu[i]) <- log(E[i]) + alpha0 + alpha1 * elev[i]/10 + alpha2 * tmin[i]/10 + b[i]
		RR[i] <- exp(alpha0 + alpha1 * elev[i]/10 + alpha2 * tmin[i]/10 + b[i])   					
		# Area-specific relative risk (for maps)
	}

	# CAR prior distribution for random effects: 
	b[1:N] ~ car.normal(adj[], weights[], num[], tau)
	for(k in 1:sumNumNeigh) {
		weights[k] <- 1
	}
	
	# Other priors:
	alpha0  ~ dflat()  
	alpha1 ~ dnorm(0.0, 1.0E-5)
	alpha2 ~ dnorm(0.0, 1.0E-5)
	tau  ~ dgamma(0.5, 0.0005) 				# prior on precision
	sigma <- sqrt(1 / tau)				# standard deviation
	        b.mean <- sum(b[])

}


list(N = 105,
O=c(1.0,16.0,2.0,2.0,1.0,1.0,1.0,2.0,1.0,3.0,1.0,1.0,2.0,1.0,1.0,1.0,1.0,2.0,1.0,1.0,2.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,3.0,1.0,1.0,1.0,1.0,2.0,3.0,1.0,2.0,1.0,1.0,2.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,2.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,2.0,1.0,2.0,1.0,1.0,1.0,1.0,1.0,2.0,2.0,1.0,8.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,2.0,3.0,1.0,1.0,2.0,1.0,1.0,2.0,1.0,2.0,1.0,1.0,1.0,1.0,2.0,2.0,1.0,131.0),
E=c(3.69,4.509,3.31,1.989,1.849,3.676,3.394,1.002,1.193,2.348,1.0,1.186,1.0,4.049,2.283,1.0,1.489,1.034,1.001,1.109,1.083,1.001,1.0,1.0,1.001,1.0,1.0,1.0,1.0,1.287,1.003,1.03,2.963,1.003,1.001,1.273,1.001,1.049,1.0,1.0,1.002,1.097,2.243,1.428,1.081,1.539,1.875,1.001,1.119,1.006,1.005,1.002,1.069,1.0,26.121,1.0,1.0,1.007,1.025,1.78,1.006,1.0,1.285,1.139,1.001,2.437,1.591,2.21,3.012,2.601,2.966,3.129,2.407,1.29,2.371,1.951,2.175,4.38,3.148,6.143,5.18,10.197,1.307,5.792,4.538,11.688,5.551,2.628,2.49,4.152,6.159,4.426,3.639,3.094,6.149,5.623,3.323,3.443,3.756,6.174,1.746,3.365,4.044,3.521,11.562),
elev=c(606,642,675,712,859,
818,715,1132,929,680,
1909,1039,1953,970,865,
2184,845,1044,2206,1108,
1276,2108,2429,2343,2368,
2318,2190,1706,1794,1509,
1682,1623,1374,1276,1757,
1147,1759,1295,1621,1519,
1318,984,873,1046,719,
937,929,1198,954,1029,
1455,1423,1086,1935,1953,
1176,1410,1611,1882,1586,
1280,1491,752,1411,1476,
716,718.,718,676,703,
674,733,1002,1066,1057,
864,1022,1077,846,995,
967,991,807,743,819,
845,789,603,612,741,
714,693,658,646,651,
645,623,688,645,708,
599,605,606,593,998), 
tmin=c(20.979296,20.873493,20.565163,20.210103,19.545126,19.981249,20.402666,16.998535,18.912335,20.430461,13.121272,18.462827,12.728333,19.372318,19.636071,12.012991,19.529143,18.0,12.239859,18.034879,17.233811,12.631108,10.89195,11.067139,11.444562,11.508896,11.647489,12.92,13.156025,16.493333,14.705285,15.464197,17.521378,16.493333,14.129119,18.070408,13.979363,17.030924,14.306667,14.372431,16.243431,18.551952,19.594483,18.609549,19.656886,19.137922,19.283816,16.617036,18.731667,17.716893,15.793333,15.793333,18.028395,13.069515,15.561563,15.775869,15.364085,15.193488,14.306667,16.39455,16.638548,13.201311,19.780959,16.771022,15.431667,20.292092,20.0977,20.244772,20.530005,20.357571,20.536146,20.298537,19.07138,18.402227,18.82009,19.593104,18.920354,18.917752,19.82144,19.368269,19.434482,19.508333,19.534791,20.42742,20.027051,20.161115,20.214211,20.817946,20.755585,20.34086,20.573682,20.571667,20.666667,20.672054,20.871667,20.871064,20.860359,20.523007,20.761097,20.628341,20.702421,20.92627,20.998786,21.011144,19.51),
num = c(6, 5, 6, 7, 9, 6, 6, 3, 6, 6, 4, 6, 5, 7, 6, 4, 2, 7, 3, 9, 6, 4, 6, 4, 3, 3, 5, 5, 3, 6, 5, 3, 2, 5, 5, 5, 7, 7, 7, 5, 5, 6, 3, 4, 6, 6, 8, 9, 5, 6, 4, 6, 7, 10, 7, 6, 6, 9, 3, 7, 5, 4, 4, 4, 1, 9, 5, 6, 5, 5, 5, 4, 4, 5, 6, 4, 5, 5, 5, 6, 4, 4, 1, 4, 4, 6, 3, 4, 4, 8, 3, 6, 4, 8, 4, 4, 4, 4, 8, 3, 2, 5, 3, 3, 6
),
adj = c(104, 103, 102, 101, 97, 2,
102, 100, 99, 97, 1,
93, 90, 89, 86, 71, 70,
86, 85, 72, 71, 70, 7, 5,
105, 85, 83, 82, 81, 72, 9, 6, 4,
105, 79, 72, 66, 7, 5,
72, 71, 69, 66, 6, 4,
65, 64, 12,
81, 80, 78, 77, 74, 5,
69, 68, 66, 63, 53, 18,
64, 62, 61, 13,
64, 63, 61, 60, 53, 8,
62, 60, 54, 25, 11,
105, 80, 79, 78, 77, 75, 15,
79, 76, 75, 67, 66, 14,
54, 28, 26, 19,
76, 73,
68, 55, 53, 50, 47, 45, 10,
28, 27, 16,
49, 47, 46, 44, 42, 38, 36, 34, 21,
44, 34, 33, 32, 31, 20,
37, 30, 29, 23,
59, 39, 37, 35, 24, 22,
58, 35, 27, 23,
54, 26, 13,
54, 25, 16,
58, 54, 28, 24, 19,
58, 54, 27, 19, 16,
31, 30, 22,
38, 37, 34, 31, 29, 22,
34, 32, 30, 29, 21,
33, 31, 21,
32, 21,
38, 31, 30, 21, 20,
59, 58, 39, 24, 23,
56, 42, 41, 38, 20,
41, 40, 39, 38, 30, 23, 22,
42, 41, 37, 36, 34, 30, 20,
59, 58, 57, 40, 37, 35, 23,
57, 56, 41, 39, 37,
56, 40, 38, 37, 36,
56, 49, 48, 38, 36, 20,
67, 46, 44,
46, 43, 21, 20,
68, 67, 66, 47, 46, 18,
67, 47, 45, 44, 43, 20,
68, 50, 49, 48, 46, 45, 20, 18,
58, 57, 56, 52, 51, 50, 49, 47, 42,
50, 48, 47, 42, 20,
55, 51, 49, 48, 47, 18,
55, 52, 50, 48,
58, 57, 55, 54, 51, 48,
68, 63, 60, 55, 18, 12, 10,
60, 58, 55, 52, 28, 27, 26, 25, 16, 13,
60, 54, 53, 52, 51, 50, 18,
57, 48, 42, 41, 40, 36,
58, 56, 52, 48, 40, 39,
57, 54, 52, 48, 39, 35, 28, 27, 24,
39, 35, 23,
62, 61, 55, 54, 53, 13, 12,
64, 62, 60, 12, 11,
61, 60, 13, 11,
69, 53, 12, 10,
61, 12, 11, 8,
8,
79, 69, 68, 67, 45, 15, 10, 7, 6,
66, 46, 45, 43, 15,
66, 53, 47, 45, 18, 10,
71, 66, 63, 10, 7,
86, 85, 71, 4, 3,
70, 69, 7, 4, 3,
7, 6, 5, 4,
76, 75, 74, 17,
78, 77, 75, 73, 9,
78, 76, 74, 73, 15, 14,
75, 73, 17, 15,
80, 78, 74, 14, 9,
77, 75, 74, 14, 9,
105, 66, 15, 14, 6,
105, 82, 81, 77, 14, 9,
82, 80, 9, 5,
105, 81, 80, 5,
5,
98, 92, 90, 87,
86, 70, 5, 4,
90, 87, 85, 70, 4, 3,
90, 86, 84,
96, 95, 94, 89,
94, 93, 88, 3,
94, 93, 92, 91, 87, 86, 84, 3,
94, 92, 90,
99, 98, 94, 91, 90, 84,
94, 90, 89, 3,
99, 96, 93, 92, 91, 90, 89, 88,
102, 99, 96, 88,
99, 95, 94, 88,
104, 103, 2, 1,
100, 99, 92, 84,
102, 100, 98, 96, 95, 94, 92, 2,
99, 98, 2,
102, 1,
101, 99, 95, 2, 1,
104, 97, 1,
103, 97, 1,
82, 80, 79, 14, 6, 5
),
sumNumNeigh=538
)



list(tau = 1, alpha0 = 0, alpha1 = 0, alpha2=0,
b=c(0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0,
0,0,0,0,0)
)

list(tau = 10, alpha0 = 1.0, alpha1 = 1.0, alpha2 =1.0, alpha3 =1.0,
b=c(1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,
1,1,1,1,1,)
)

list(tau = 10, alpha0 = 1.0, alpha1 = 1.0)






