Parameter

Model 1

Parameter

Model 2

Parameter

Model 3

Parameter

Model 4

Parameter

Model 5


α

N(0,0.01)

α

N(0,0.01)

α

N(0,0.01)

α

N(0,0.01)

α

N(0,0.01)

β_{j};j = 1,…,7

CAR(1/Ƭ_{βj},R)

β_{j};j = 1,…,7

N(0,1/ Ƭ_{βj})

β_{j};j = 1,…,7

N(0,σ^{2}_{βj})

β_{j};j = 1,…,7

N(0,1/ Ƭ_{βj})

β_{j};j = 1,…,7

N(0,1/ Ƭ_{βj})

U_{i};i = 1,…,N

N(α,1/Ƭ_{U})

U_{i};i = 1,…,N

N(α,1/ Ƭ_{U})

U_{i};i = 1,…,N

N(α,σ^{2}_{U})

U_{i};i = 1,…,N

N(α,1/ Ƭ_{U})

U_{i};i = 1,…,N

N(α,1/ Ƭ_{U})

S_{i};i = 1,…,N

CAR(1/Ƭ_{S},R)

S_{i};i = 1,…,N

CAR(1/Ƭ_{S},R)

S_{i};i = 1,…,N

CAR((σ^{2}_{S},R)

S_{i};i = 1,…,N

CAR(1/Ƭ_{S},R)

S_{i};i = 1,…,N

CAR(1/Ƭ_{S},R)

Ƭ_{βj}

Ga(1,0.01)

Ƭ_{βj}

Ga(1,0.01)

σ_{βj}

U(0.01,5)

Ƭ_{βj}

Ga(1,0.01)

Ƭ_{βj}

Ga(1,0.01)

Ƭ_{U}

Ga(1,0.01)

Ƭ_{U}

Ga(1,0.01)

σ_{U}

U(0.01,5)

σ_{U}

N(0,0.0625)I(0,)

log(σ_{U})

N(0,4)

Ƭ_{S}

Ga(1,0.01)

Ƭ_{S}

Ga(1,0.01)

σ_{S}

U(0.01,5)

Ƭ_{S}

Ga(1,0.01)

Ƭ_{S}

Ga(1,0.01)

 α = intercept, j = covariates 1 to 7, β_{j} = vector of coefficients for covariates 1 to 7, i = Local Government Areas (LGAs) 1 to 71, U_{i} = uncorrelated residual error for LGAs 1 to 71, S_{i} = correlated residual error for LGAs 1 to 71, Ƭ_{βj} = vector of precisions for covariate coefficients, Ƭ_{U} = vector of precisions for uncorrelated residual error, Ƭ_{S} = vector of precisions for correlated residual error, σ_{βj} = vector of standard deviations for covariate coefficients, σ_{U} = vector of standard deviations for uncorrelated residual error, σ_{S} = vector of standard deviations for correlated residual error, Ga = Gamma distribution, U = Uniform distribution, CAR = CAR normal prior centred around zero, denoted CAR(variance, adjacency neighbourhood weight matrix), R = adjacency neighbourhood weight matrix with diagonal entries equal to number of neighbours; ie. R_{
ii
} = m_{
i
}.