model {
for(i in 1:73) {
Y[i] ~ dpois(lambda[i])
log(lambda[i]) <- log(t[i]) + beta + S[i]
}
# spatial field representing true log contamination intensity
S[1:73] ~ spatial.exp(mu[], x[], y[],
tau, phi, kappa)
for(i in 1:73) {
mu[i] <- 0
}
# mean log contamination intensity
beta ~ dunif(-3, 7)
# priors on parameters of spatial covariance matrix
phi ~ dunif(0, 120)
kappa ~ dunif(0.1, 1.95)
sigma ~ dnorm(0, 1)I(0,)
tau <- 1/pow(sigma, 2)
for(j in 1:93) { # prediction
T[j] ~ spatial.unipred(mu.pred[j], x.pred[j],
y.pred[j], S[])
exp.T[j] <- exp(T[j] + beta) # predicted intensity
mu.pred[j] <- 0
}
# combine observed and predicted locations
for(i in 1:73) {
pred[i] <- exp(S[i])
}
for(i in 74:166) {
pred[i] <- exp.T[i-73]
}
# max value of contamination
max.level <- ranked(pred[], 166)
for(i in 1:166) { # location of maximum
pred.rank[i] <- rank(pred[], i)
prob.max[i] <- equals(pred.rank[i], 166)
}
# prob that count/sec > 15 at location i
for(i in 1:166) {
prob.exceeds.15[i] <- step(pred[i] - 15)
}
}
Inits:
list(beta = 1.5, sigma = 1, phi = 10, kappa = 0.7)
Data:
list(
x = c(-4.033, -4.033, -3.95, -3.95, -3.867, -3.867,
-3.75, -3.8, -3.8, -3.8, -3.8, -3.8, -3.773, -3.773, -3.773,
-3.773, -3.773, -3.747, -3.747, -3.747, -3.747, -3.747, -3.72,
-3.72, -3.72, -3.72, -3.72, -3.693, -3.693, -3.693, -3.693, -3.693,
-3.633, -3.633, -3.553, -3.553, -3.553, -3.553, -3.553, -3.527,
-3.527, -3.527, -3.527, -3.527, -3.5, -3.5, -3.5, -3.5, -3.5,
-3.473, -3.473, -3.473, -3.473, -3.473, -3.447, -3.447, -3.447,
-3.447, -3.447, -3.367, -3.367, -3.267, -3.267, -3.133, -3, -3,
-2.867, -2.733, -2.6, -2.467, -2.333, -2.2, -2.067),
y = c(-2.18, -2.11, -2.213, -2.11, -2.233, -2.11, -2.233, -2.173, -2.147,
-2.12, -2.093, -2.067, -2.173, -2.147, -2.12, -2.093, -2.067,
-2.173, -2.147, -2.12, -2.093, -2.067, -2.173, -2.147, -2.12,
-2.093, -2.067, -2.173, -2.147, -2.12, -2.093, -2.067, -2.233,
-2.11, -2.287, -2.26, -2.233, -2.207, -2.18, -2.287, -2.26, -2.233,
-2.207, -2.18, -2.287, -2.26, -2.233, -2.207, -2.18, -2.287,
-2.26, -2.233, -2.207, -2.18, -2.287, -2.26, -2.233, -2.207,
-2.18, -2.2, -2.11, -2.133, -2.067, -2.017, -2, -1.947, -1.907,
-1.807, -1.773, -1.707, -1.673, -1.64, -1.627),
Y = c(75, 371,1931, 4357, 2114, 2318, 1975, 1912, 1902, 1882, 3017, 2403, 2616,
2275, 2432, 2754, 3452, 1726, 2118, 2269, 4629, 1840, 2691, 4084,
2187, 4531, 2022, 1822, 2800, 2722, 4083, 1650, 2890, 2776, 2525,
3580, 2960, 3100, 3611, 1813, 2560, 3733, 2273, 3437, 2603, 2148,
2360, 3050, 3287, 2603, 4044, 2560, 3019, 2407, 2735, 3020, 2215,
3414, 1688, 3447, 1091, 3279, 3101, 2370, 2902, 1401, 892, 1872,
2610, 3548, 2652, 2625, 2314),
t = c(300, 300, 300, 300, 300,
300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 400,
300, 300, 400, 300, 360, 300, 400, 300, 300, 300, 300, 300, 300,
400, 300, 300, 300, 300, 300, 300, 300, 200, 300, 300, 300, 300,
300, 200, 300, 300, 300, 300, 300, 300, 300, 300, 200, 300, 300,
300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300,
300, 300, 300),
x.pred = c(-4.173, -4.12, -4.12, -4.12, -4.066,
-4.066, -4.066, -4.013, -4.013, -4.013, -3.96, -3.96, -3.96,
-3.906, -3.906, -3.906, -3.906, -3.906, -3.906, -3.853, -3.853,
-3.853, -3.853, -3.8, -3.8, -3.8, -3.8, -3.746, -3.746, -3.693,
-3.693, -3.693, -3.693, -3.64, -3.64, -3.64, -3.64, -3.586, -3.586,
-3.586, -3.586, -3.586, -3.533, -3.533, -3.48, -3.48, -3.426,
-3.426, -3.373, -3.373, -3.32, -3.32, -3.32, -3.32, -3.266, -3.266,
-3.213, -3.213, -3.213, -3.16, -3.106, -3.106, -3.106, -3.053,
-3.053, -2.946, -2.893, -2.84, -2.84, -2.786, -2.733, -2.68,
-2.68, -2.573, -2.573, -2.52, -2.52, -2.413, -2.413, -2.36, -2.306,
-2.306, -2.253, -2.253, -2.2, -2.146, -2.146, -2.093, -2.093,
-2.04, -2.04, -1.986, -1.986),
y.pred = c(-2.095, -2.042, -2.095,
-2.148, -2.042, -2.095, -2.148, -1.988, -2.042, -2.148, -1.988,
-2.042, -2.148, -1.988, -2.042, -2.095, -2.148, -2.201, -2.255,
-1.988, -2.042, -2.148, -2.201, -1.988, -2.201, -2.255, -2.308,
-2.201, -2.308, -2.201, -2.255, -2.308, -2.361, -2.042, -2.148,
-2.201, -2.361, -2.095, -2.148, -2.201, -2.255, -2.308, -2.095,
-2.148, -2.095, -2.148, -2.095, -2.148, -2.148, -2.255, -2.042,
-2.095, -2.148, -2.201, -1.988, -2.095, -1.988, -2.042, -2.095,
-1.988, -1.935, -1.988, -2.042, -1.935, -1.988, -1.935, -1.935,
-1.828, -1.882, -1.828, -1.775, -1.775, -1.828, -1.722, -1.775,
-1.722, -1.775, -1.668, -1.722, -1.722, -1.615, -1.668, -1.615,
-1.668, -1.668, -1.615, -1.668, -1.562, -1.668, -1.562, -1.615,
-1.562, -1.615))
node mean sd MC error 2.5% median 97.5% start sample
beta 1.841 0.3141 0.014 1.228 1.856 2.491 10001 250000
kappa 0.9327 0.2239 0.002256 0.4973 0.9317 1.368 10001 250000
max.level 32.72 12.44 0.08155 18.93 29.82 63.6 10001 250000
phi 8.547 6.106 0.1143 1.008 7.58 21.0 10001 250000
sigma 0.8377 0.2211 0.004254 0.5677 0.787 1.413 10001 250000
node mean sd MC error 2.5% median 97.5% start sample
beta 1.873 0.3431 0.01078 1.242 1.869 2.673 10001 1000000
kappa 0.9312 0.2246 0.001621 0.4954 0.9301 1.369 10001 1000000
max.level 32.83 12.58 0.0579 18.99 29.88 64.09 10001 1000000
phi 8.445 6.092 0.08313 0.8851 7.485 20.88 10001 1000000
sigma 0.8459 0.2311 0.00342 0.5683 0.7903 1.452 10001 1000000