lip_cancer.data.R

N <- 56
O <- c( 9, 39, 11, 9, 15, 8, 26, 7, 6, 20,
        13, 5, 3, 8, 17, 9, 2, 7, 9, 7,
        16, 31, 11, 7, 19, 15, 7, 10, 16, 11,
        5, 3, 7, 8, 11, 9, 11, 8, 6, 4,
        10, 8, 2, 6, 19, 3, 2, 3, 28, 6,
        1, 1, 1, 1, 0, 0)
E <- c( 1.4, 8.7, 3.0, 2.5, 4.3, 2.4, 8.1, 2.3, 2.0, 6.6,
        4.4, 1.8, 1.1, 3.3, 7.8, 4.6, 1.1, 4.2, 5.5, 4.4,
        10.5,22.7, 8.8, 5.6,15.5,12.5, 6.0, 9.0,14.4,10.2,
        4.8, 2.9, 7.0, 8.5,12.3,10.1,12.7, 9.4, 7.2, 5.3,
        18.8,15.8, 4.3,14.6,50.7, 8.2, 5.6, 9.3,88.7,19.6,
        3.4, 3.6, 5.7, 7.0, 4.2, 1.8)
x <- c(16,16,10,24,10,24,10, 7, 7,16,
        7,16,10,24, 7,16,10, 7, 7,10,
        7,16,10, 7, 1, 1, 7, 7,10,10,
        7,24,10, 7, 7, 0,10, 1,16, 0,
        1,16,16, 0, 1, 7, 1, 1, 0, 1,
        1, 0, 1, 1,16,10)
A <- structure(c(0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 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, 1, 0, 0, 1, 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, 1, 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,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0,
1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1,
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, 1, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 1, 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, 1, 0, 1, 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, 1, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 1, 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, 1, 1, 0, 0, 1, 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, 1, 0, 0, 0, 1, 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, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,
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,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 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, 1, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0,
0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 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,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0,
1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 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, 1, 0, 0, 0, 1, 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, 1, 1, 0, 0,
0, 0, 1, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0,
0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 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, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 1, 0, 0, 0, 1, 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, 1, 0,
0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 1, 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, 1,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 1, 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, 1, 0, 1, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 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, 1, 0, 0, 0, 1, 0, 1, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 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, 1,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 1, 1, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 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, 1,
0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 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, 1, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0,
1, 1, 0, 1, 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, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1,
0, 0, 1, 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, 1, 0), .Dim = c(N, N))

lip_cancer.init.R

init <-
      list(
            list(
                  alpha0 = 0.0,
                  alpha1 = 0.0,
                  beta1 = rep(0, 56),
                  tau = 1.0,
                  p = 0.5
            )
      )

lip_cancer_sparse.data.R

# num obs
N <- 56

# observed
O <- c( 9, 39, 11, 9, 15, 8, 26, 7, 6, 20,
        13, 5, 3, 8, 17, 9, 2, 7, 9, 7,
        16, 31, 11, 7, 19, 15, 7, 10, 16, 11,
        5, 3, 7, 8, 11, 9, 11, 8, 6, 4,
        10, 8, 2, 6, 19, 3, 2, 3, 28, 6,
        1, 1, 1, 1, 0, 0)

# expected
E <- c( 1.4, 8.7, 3.0, 2.5, 4.3, 2.4, 8.1, 2.3, 2.0, 6.6,
        4.4, 1.8, 1.1, 3.3, 7.8, 4.6, 1.1, 4.2, 5.5, 4.4,
        10.5,22.7, 8.8, 5.6,15.5,12.5, 6.0, 9.0,14.4,10.2,
        4.8, 2.9, 7.0, 8.5,12.3,10.1,12.7, 9.4, 7.2, 5.3,
        18.8,15.8, 4.3,14.6,50.7, 8.2, 5.6, 9.3,88.7,19.6,
        3.4, 3.6, 5.7, 7.0, 4.2, 1.8)

# covariate
x <- c(16,16,10,24,10,24,10, 7, 7,16,
        7,16,10,24, 7,16,10, 7, 7,10,
        7,16,10, 7, 1, 1, 7, 7,10,10,
        7,24,10, 7, 7, 0,10, 1,16, 0,
        1,16,16, 0, 1, 7, 1, 1, 0, 1,
        1, 0, 1, 1,16,10)

# adjacency matrix
A <- structure(c(0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 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, 1, 0, 0, 1, 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, 1, 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,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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1, 1, 0, 1, 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,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1,
0, 0, 1, 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, 1, 0), .Dim = c(N, N))

# diagonal (counts of neighbors)
D <- rowSums(A)

# sparse version of A
A_sparse <- which(A == 1, arr.ind=TRUE)
A_N <- dim(A_sparse)[1]
A1 <- A_sparse[,1]
A2 <- A_sparse[,2]

# how many linearly spaced values of p [0,1] to take for log(determinant(D - p * A))
p_samples <- 1000

lp_method.stan

// Author:  Kyle Foreman (kforeman@post.harvard.edu)
// Date:    24 February 2013
// attempt to replicate GeoBUGS "lip cancer" CAR example (http://www.openbugs.info/Manuals/GeoBUGS/Examples/Scotland.html)
// data from http://www.openbugs.info/Manuals/GeoBUGS/Examples/Scotlanddata.html (with adjacency matrix A converted to dense)
// following GMRF formulation of CAR from section 2.1 of http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2724012/

data {
    int<lower=1> N;     // number of areas
    int O[N];           // observed cases
    vector[N] E;        // expected cases
    vector[N] x;        // covariate (pct agric)
    matrix[N,N] A;      // area adjacency matrix
}

transformed data {
    matrix[N,N] D;      // diagonal matrix with d_ii = sum(c_ij)
    vector[N] zeros;    // zeros for mean of MVN
    for (i in 1:N)
        for (j in 1:N)
            D[i,j] <- if_else(i==j, sum(row(A, i)), 0.0);
    for (i in 1:N)
        zeros[i] <- 0;
}

parameters {
    real alpha0;            // intercept
    real alpha1;            // coefficient on covariate
    vector[N] beta1;        // area-specific random effect (CAR)
    real<lower=1e-5> tau;   // precision of CAR
    real<lower=0,upper=1> p;// strength of spatial correlation
}

transformed parameters {
    real sigma_sq;
    sigma_sq <- 1.0 / tau;
}

model {
    // declarations
        real beta1_mean;
        vector[N] beta1_stz;
        vector[N] log_mu;
    // priors on model parameters
        // no explicit prior on alpha0 (improper flat prior)
        alpha1 ~ normal(0.0, sqrt(1e5));
        tau ~ gamma(0.5, 0.0005);
    // Ben's MVN replacement
        lp__ <- lp__ - 0.5 / sigma_sq * (beta1' * D * beta1 - p * (beta1' * A * beta1));
        lp__ <- lp__ - 0.5 * N * log(sigma_sq) + 0.5 * log_determinant(D - p * A);
    // impose sum-to-zero constraint on CAR
        beta1_mean <- mean(beta1);
        beta1_stz <- beta1 - beta1_mean;
    // model prediction
        log_mu <- log(E) + alpha0 + alpha1 * x + beta1_stz;
    // likelihood
        O ~ poisson_log(log_mu);
}

multi_normal_prec.stan

// Author:  Kyle Foreman (kforeman@post.harvard.edu)
// Date:    24 February 2013
// attempt to replicate GeoBUGS "lip cancer" CAR example (http://www.openbugs.info/Manuals/GeoBUGS/Examples/Scotland.html)
// data from http://www.openbugs.info/Manuals/GeoBUGS/Examples/Scotlanddata.html (with adjacency matrix A converted to dense)
// following GMRF formulation of CAR from section 2.1 of http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2724012/

data {
    int<lower=1> N;     // number of areas
    int O[N];           // observed cases
    vector[N] E;        // expected cases
    vector[N] x;        // covariate (pct agric)
    matrix[N,N] A;      // area adjacency matrix
}

transformed data {
    matrix[N,N] D;      // diagonal matrix with d_ii = sum(c_ij)
    vector[N] zeros;    // zeros for mean of MVN
    for (i in 1:N)
        for (j in 1:N)
            D[i,j] <- if_else(i==j, sum(row(A, i)), 0.0);
    for (i in 1:N)
        zeros[i] <- 0.0;
}

parameters {
    real alpha0;            // intercept
    real alpha1;            // coefficient on covariate
    vector[N] beta1;        // area-specific random effect (CAR)
    real<lower=1e-5> tau;   // precision of CAR
    real<lower=0,upper=1> p;// strength of spatial correlation
}

transformed parameters {
    real sigma_sq;
    sigma_sq <- 1.0 / tau;
}

model {
    // declarations
        matrix[N,N] Tau;  // precision matrix for CAR
        real beta1_mean;
        vector[N] beta1_stz;
        vector[N] log_mu;
    // priors on model parameters
        // no explicit prior on alpha0 (improper flat prior)
        alpha1 ~ normal(0.0, sqrt(1e5));
        tau ~ gamma(0.5, 0.0005);
    // precision matrix
        Tau <- tau * (D - p * A);
    // CAR model using precision version of MVN
        beta1 ~ multi_normal_prec(zeros, Tau);
    // impose sum-to-zero constraint on CAR
        beta1_mean <- mean(beta1);
        beta1_stz <- beta1 - beta1_mean;
    // model prediction
        log_mu <- log(E) + alpha0 + alpha1 * x + beta1_stz;
    // likelihood
        O ~ poisson_log(log_mu);
}

run_models.R

# Author:   Kyle Foreman (kforeman@post.harvard.edu)
# Date:     13 Sep 2013
# Purpose:  compare different parameterizations of the CAR model


library(rstan)

# set working directory if not done already...
if (Sys.getenv('USER') == 'kforeman') setwd('~/Dropbox/USCOD/models/LipCancer')

# data
model_data <- new.env()
sys.source('lip_cancer.data.R', model_data)

# initial values
source('lip_cancer.init.R')

# lp__ method
if (TRUE) # this is so you can compile separately from sampling - makes it so you can better compare times and rerun more efficiently
lp_method_dso <- stan(file='lp_method.stan', init=init, data=model_data, iter=1, chains=1)
if (TRUE)
lp_method_time <- system.time(lp_method_fit <-
      stan(
            fit = lp_method_dso,
            data = model_data,
            init = init,
            chains = 1,
            iter = 10e3
      )
)

# precision matrix method
if (TRUE)
multi_normal_prec_dso <- stan(file='multi_normal_prec.stan', init=init, data=model_data, iter=1, chains=1)
if (TRUE)
multi_normal_prec_time <- system.time(multi_normal_prec_fit <-
      stan(
            fit = multi_normal_prec_dso,
            data = model_data,
            init = init,
            chains = 1,
            iter = 10e3
      )
)

# sparse data
sparse_data <- new.env()
sys.source('lip_cancer_sparse.data.R', sparse_data)

# sparse method
if (TRUE)
sparse_dso <- stan(file='sparse_lp.stan', init=init, data=sparse_data, iter=1, chains=1)
if (TRUE)
sparse_time <- system.time(sparse_fit <-
      stan(
            fit = sparse_dso,
            data = sparse_data,
            init = init,
            chains = 1,
            iter = 10e3
      )
)

# compare parameter values
params <- data.frame(cbind(summary(multi_normal_prec_fit)$summary[,1], summary(lp_method_fit)$summary[,1], summary(sparse_fit)$summary[,1]))
names(params) <- c('multi_normal_prec', 'lp_method', 'sparse')
print(params)

# compare sampling time
time <- data.frame(t(c(multi_normal_prec_time['user.self'], lp_method_time['user.self'], sparse_time['user.self'])))
names(time) <- c('multi_normal_prec', 'lp_method', 'sparse')
print(time)

sparse_lp.stan

// Author:  Kyle Foreman (kforeman@post.harvard.edu)
// Date:    12 Sep 2013
// GeoBUGS "lip cancer" CAR example (http://www.openbugs.info/Manuals/GeoBUGS/Examples/Scotland.html)
// following GMRF formulation of CAR from section 2.1 of http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2724012/

data {
    int<lower=1> N;     // number of areas
    int O[N];           // observed cases
    vector[N] E;        // expected cases
    vector[N] x;        // covariate (pct agric)
    int<lower=1> A_N;   // number of non-zero elements of adjacency matrix
    int A1[A_N];    // sparse representation of adjacency matrix
    int A2[A_N];    // sparse representation of adjacency matrix
    vector[N] D;    // counts of neighbors for each
    int p_samples;  // number of samples of p to take
}

transformed data {
    vector[N] zeros;    // zeros for mean of MVN
    matrix[N,N] DpA;    // D - p * A
    vector[p_samples + 1] ldet_DpA; // sampled values of log(determinant(D - p * A))
    for (i in 1:N)
        zeros[i] <- 0.0;
    # the diagonal of D - p * A is just count(i_neighbors)
    for (i in 1:N)
        for (j in 1:N)
            DpA[i,j] <- if_else(i==j, D[i], 0.0);
    # calculate the off diagonal of D - p * A for each value of p
    for (i in 1:(p_samples + 1)) {
        for (j in 1:A_N)
            DpA[A1[j], A2[j]] <- -1.0 * ((i - 1.0) / p_samples);
        # store the sampled log(determinant(D - p * A))
        ldet_DpA[i] <- log_determinant(DpA);
    }
}

parameters {
    real alpha0;            // intercept
    real alpha1;            // coefficient on covariate
    vector[N] beta1;        // area-specific random effect (CAR)
    real<lower=1e-5> tau;   // precision of CAR
    real<lower=0,upper=1> p;// strength of spatial correlation
}

transformed parameters {
    real sigma_sq;
    sigma_sq <- 1.0 / tau;
}

model {
    // declarations
        real beta1_mean;
        vector[N] beta1_stz;
        vector[N] log_mu;
        row_vector[N] beta1t_A;
        row_vector[N] beta1t_D;
        real ldet_left;
        real ldet_right;
        int idx;
    // priors on model parameters
        // no explicit prior on alpha0 (improper flat prior)
        alpha1 ~ normal(0.0, sqrt(1e5));
        tau ~ gamma(0.5, 0.0005);
    // beta1" * A
        for (i in 1:N)
            beta1t_A[i] <- 0.0; # initialize vector
        for (i in 1:A_N)
            beta1t_A[A1[i]] <- beta1t_A[A1[i]] + beta1[A2[i]];
    // beta1' * D
        for (i in 1:N)
            beta1t_D[i] <- beta1[i] * D[i];
    // Ben's MVN replacement
        lp__ <- lp__ - 0.5 / sigma_sq * (beta1t_D * beta1 - p * (beta1t_A * beta1));
        lp__ <- lp__ - 0.5 * N * log(sigma_sq);
        # hacky interpolated log(determinant(D - p * A))
        idx <- 0;
        while (floor(p * p_samples) >= idx) {
            idx <- idx + 1;
        }
        ldet_left <- ldet_DpA[idx];
        ldet_right <- ldet_DpA[idx + 1];
        lp__ <- lp__ + 0.5 * (ldet_left + (ldet_right - ldet_left) * (p * p_samples - floor(p * p_samples)));;
    // impose sum-to-zero constraint on CAR
        beta1_mean <- mean(beta1);
        beta1_stz <- beta1 - beta1_mean;
    // model prediction
        log_mu <- log(E) + alpha0 + alpha1 * x + beta1_stz;
    // likelihood
        O ~ poisson_log(log_mu);
}