We fit the following model, allowing a convolution prior for the random effects:

O

log μ

The code for this model is given below.

Model

model {

for (i in 1 : N) {

# Likelihood

O[i] ~ dpois(mu[i])

log(mu[i]) <- log(E[i]) + alpha + beta * depriv[i] + b[i] + h[i]

# Area-specific relative risk (for maps)

RR[i] <- exp(alpha + beta * depriv[i] + b[i] + h[i])

# Exchangeable prior on unstructured random effects

h[i] ~ dnorm(0, tau.h)

}

# CAR prior distribution for spatial random effects:

b[1 : N] ~ car.normal(adj[], weights[], num[], tau.b)

for(k in 1:sumNumNeigh) {

weights[k] <- 1

}

# Other priors:

alpha ~ dflat()

beta ~ dnorm(0.0, 1.0E-5)

tau.b ~ dgamma(0.5, 0.0005)

sigma.b <- sqrt(1 / tau.b)

tau.h ~ dgamma(0.5, 0.0005)

sigma.h <- sqrt(1 / tau.h)

}

```
list(N = 44,
```

O = c(4, 8, 3, 6, 2, 7, 7, 2, 10, 13, 5, 7, 9, 3, 3, 1, 2, 3, 19, 7, 5, 4,

9, 2, 4, 6, 14, 13, 6, 7, 9, 3, 4, 10, 10, 8, 23, 24, 18, 10, 6, 4, 17, 7),

E = c(7.20902956, 7.81436792, 3.46693788, 7.04393728, 7.37412184,

4.45749156, 6.3285374, 4.45749156, 6.3285374, 6.76878348, 9.30019844,

6.6036912, 3.17289144, 1.68706092, 4.43859892, 6.6036912, 7.26406032,

6.21847588, 7.31909108, 6.21847588, 7.04393728, 5.2934088044,

10.370546722, 6.58993351, 6.1573917364, 7.6701873288, 13.9359896624,

12.7473252464, 6.2658023336, 10.96487893, 8.5341702608, 6.1034615916,

6.6977937996, 8.9661617268, 8.8043712924, 8.3723798264, 15.3166165772,

15.7486080432, 17.6933951016, 8.642580858, 4.969277628, 6.3736626232,

11.2890101064, 6.3736626232),

depriv = c(1.233, 8.162, 0.919, -0.78, -1.182, 3.647, 6.47, 0.948, 4.479,

11.739, -0.125, 0.063, 4.392, -1.021,-0.609, 1.896, -0.053, 1.043, -0.899,

8.441, 5.81, 3.575, 5.78, -0.375, 4.828, 1.668, 4.97, 10.21, -0.234, 7.804,

5.544, -1.699, 7.029, 2.581, 0.958, 2.811, 6.376, 8.627, 1.139, 3.169, 3.332,

2.754, 7.55, 3.961),

num = c(5, 4, 6, 7, 4, 5, 6, 6, 3, 6,

5, 3, 4, 5, 6, 6, 5, 3, 5, 3,

2, 4, 4, 6, 6, 3, 3, 6, 4, 4,

8, 9, 5, 7, 3, 3, 2, 4, 5, 5,

5, 3, 8, 6

),

adj = c(

17, 12, 9, 8, 4,

14, 13, 10, 7,

32, 17, 15, 11, 8, 6,

33, 32, 17, 16, 14, 12, 1,

21, 19, 15, 6,

19, 15, 11, 5, 3,

43, 16, 14, 13, 10, 2,

18, 17, 15, 9, 3, 1,

18, 8, 1,

43, 38, 20, 13, 7, 2,

32, 24, 19, 6, 3,

14, 4, 1,

20, 10, 7, 2,

16, 12, 7, 4, 2,

21, 18, 8, 6, 5, 3,

43, 33, 23, 14, 7, 4,

32, 8, 4, 3, 1,

15, 9, 8,

27, 24, 11, 6, 5,

38, 13, 10,

15, 5,

44, 39, 26, 25,

43, 33, 31, 16,

41, 40, 32, 27, 19, 11,

44, 39, 34, 31, 28, 22,

44, 39, 22,

40, 24, 19,

39, 35, 34, 31, 29, 25,

36, 35, 34, 28,

43, 38, 36, 34,

44, 43, 34, 33, 32, 28, 25, 23,

44, 41, 33, 31, 24, 17, 11, 4, 3,

32, 31, 23, 16, 4,

43, 36, 31, 30, 29, 28, 25,

39, 29, 28,

34, 30, 29,

42, 40,

43, 30, 20, 10,

35, 28, 26, 25, 22,

42, 41, 37, 27, 24,

44, 42, 40, 32, 24,

41, 40, 37,

38, 34, 31, 30, 23, 16, 10, 7,

41, 32, 31, 26, 25, 22

),

sumNumNeigh = 212

)

```
list(tau.b = 0.5, tau.h = 0.2, alpha=0, beta=0)
```

```
list(tau.b = 1.0, tau.h = 1.0, alpha=1.0, beta=1.0)
```