Table 5: Posterior mean estimate of the model parameters and the corresponding 95% CI under varying starting values and prior distributions for 𝛽 0 and 𝑢 𝑟 𝑡 .

Prior for 𝑢 𝑟 𝑡
Prior for 𝛽 0 Starting valuesParameterIntrinsic CAR prior Laplace CAR prior
Mean(95% CI)Mean(95% CI)

flat( ) e x p ( 𝛽 0 ) 0.936 ( 0 . 7 2 4 , 1 . 1 2 6 ) 0.947 ( 0 . 7 8 7 , 1 . 1 1 6 )
t t [ 1 ] , 𝑢 [ 1 ] , 𝜏 𝜉 = 0 . 1 𝜎 t t 0.082 ( 0 . 0 1 6 , 0 . 2 8 1 ) 0.073 ( 0 . 0 1 6 , 0 . 2 2 5 )
𝜎 𝑢 0.744 ( 0 . 6 0 5 , 0 . 9 0 4 ) 0.920 ( 0 . 8 0 9 , 1 . 0 4 3 )
e x p ( 𝛽 0 ) 0.962 ( 0 . 7 4 5 , 1 . 2 1 7 ) 0.949 ( 0 . 7 8 7 , 1 . 1 2 0 )
t t [ 2 ] , 𝑢 [ 2 ] , 𝜏 𝜉 = 0 . 0 1 𝜎 t t 0.091 ( 0 . 0 1 6 , 0 . 3 2 4 ) 0.069 ( 0 . 0 1 6 , 0 . 2 1 3 )
𝜎 𝑢 0.744 ( 0 . 6 0 5 , 0 . 9 0 3 ) 0.920 ( 0 . 8 1 0 , 1 . 0 4 3 )
e x p ( 𝛽 0 ) 0.941 ( 0 . 6 8 4 , 1 . 1 5 4 ) 0.970 ( 0 . 7 9 2 , 1 . 1 7 6 )
t t [ 3 ] , 𝑢 [ 3 ] , 𝜏 𝜉 = 0 . 0 0 1 𝜎 t t 0.089 ( 0 . 0 1 6 , 0 . 3 1 2 ) 0.079 ( 0 . 0 1 6 , 0 . 2 6 3 )
𝜎 𝑢 0.744 ( 0 . 6 0 6 , 0 . 9 0 4 ) 0.920 ( 0 . 8 0 9 , 1 . 0 4 2 )

e x p ( 𝛽 0 ) 0.947 ( 0 . 7 2 7 , 1 . 1 5 6 ) 0.950 ( 0 . 7 6 6 , 1 . 1 4 6 )
𝑁 ( 0 , 1 . 0 5 ) t t [ 1 ] , 𝑢 [ 1 ] , 𝜏 𝜉 = 0 . 1 𝜎 t t 0.085 ( 0 . 0 1 6 , 0 . 2 9 1 ) 0.081 ( 0 . 0 1 6 , 0 . 2 5 0 )
𝜎 𝑢 0.744 ( 0 . 6 0 6 , 0 . 9 0 4 ) 0.920 ( 0 . 8 0 9 , 1 . 0 4 3 )
e x p ( 𝛽 0 ) 0.947 ( 0 . 7 2 1 , 1 . 1 6 4 ) 0.956 ( 0 . 7 5 2 , 1 . 1 8 2 )
t t [ 2 ] , 𝑢 [ 2 ] , 𝜏 𝜉 = 0 . 0 1 𝜎 t t 0.087 ( 0 . 0 1 6 , 0 . 2 9 9 ) 0.089 ( 0 . 0 1 6 , 0 . 3 1 2 )
𝜎 𝑢 0.744 ( 0 . 6 0 6 , 0 . 9 0 4 ) 0.920 ( 0 . 8 0 9 , 1 . 0 4 3 )
e x p ( 𝛽 0 ) 0.953 ( 0 . 7 5 1 , 1 . 1 6 9 ) 0.957 ( 0 . 7 5 7 , 1 . 2 2 0 )
t t [ 3 ] , 𝑢 [ 3 ] , 𝜏 𝜉 = 0 . 0 0 1 𝜎 t t 0.083 ( 0 . 0 1 6 , 0 . 2 7 7 ) 0.080 ( 0 . 0 1 6 , 0 . 2 6 5 )
𝜎 𝑢 0.743 ( 0 . 6 0 6 , 0 . 9 0 3 ) 0.921 ( 0 . 8 0 9 , 1 . 0 4 4 )