################  STATISTICAL MODEL   ###############
model{
  #Likelihood
  for(i in 1:100){
      MV[i]~dnorm(mu[i],taue)
      mu[i]<-int+INDUS[i]*beta[1] + NOX[i]*beta[2] +  RM[i]*beta[3] +  
                  TAX[i]*beta[4] + PT[i]*beta[5] + LSTAT[i]*beta[6]
  }
  int~dnorm(0,0.01)
  taue~dgamma(0.1,0.1)

  #Mixture prior for the regression coefficients
  for(j in 1:6){    
    beta[j]~dnorm(0,prec[j])
    prec[j]<-1/var[j]
    var[j]<-(1-gamma[j])*0.001 + gamma[j]*10
    gamma[j]~dbern(0.5)
  }
}

###################    BOSTON HOUSING DATA    ################
list(
 MV=c(24.0, 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15.0, 18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6, 15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21.0, 12.7, 14.5, 13.2, 13.1, 13.5, 18.9, 20.0, 21.0, 24.7, 30.8, 34.9, 26.6, 25.3, 24.7, 21.2, 19.3, 20.0, 16.6, 14.4, 19.4, 19.7, 20.5, 25.0, 23.4, 18.9, 35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16.0, 22.2, 25.0, 33.0, 23.5, 19.4, 22.0, 17.4, 20.9, 24.2, 21.7,
22.8, 23.4, 24.1, 21.4, 20.0, 20.8, 21.2, 20.3, 28.0, 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2, 23.6, 28.7, 22.6, 22.0, 22.9, 25.0, 20.6, 28.4, 21.4, 38.7, 43.8, 33.2),

 INDUS=c(-1.378, 0.127, 0.127, -1.419, -1.419, -1.419, 0.380, 0.380, 0.380, 0.380, 0.380, 0.380, 0.380, 0.465, 0.465, 0.465, 0.465,  0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, 0.465, -0.224, -0.224, -0.224, -0.224, -1.176, -1.176, 0.076, 0.076, 0.076, 0.076, 0.076, 0.076, 0.076, 0.076, 0.076, -0.325, -0.325, -0.325, -0.325, -0.844, -1.723, -1.875, -1.691, -0.487, -0.487, -0.487, -0.487, -0.487, -0.487, -1.672, -1.043, -1.043, -0.189, -0.189, -0.189, 1.310, 1.310, 1.310, 1.310, 1.948, 1.948, 1.948, 1.948, 1.948, 1.948, -0.572, -0.572, -0.572, -0.572, -0.689 , -0.689, -0.689, -0.689, -1.030, -1.030, -1.030, -1.030, 2.647, 2.647, 2.647, -1.195, -1.195, -1.195, -1.195, -1.195),

 NOX=c(1.424, -0.050, -0.050, -0.284, -0.284, -0.284, 1.125, 1.125, 1.125, 1.125, 1.125, 1.125, 1.125, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 1.424, 0.591, 0.591, 0.591, 0.591, -0.925, -0.925, -0.498, -0.498, -0.498, -0.498, -0.498, -0.498, -0.498, -0.498, -0.498, -0.690, -0.690, -0.690, -0.690, -1.309, -1.459, -1.309, -1.288, -0.391, -0.391, -0.391, -0.391, -0.391, -0.391, -1.179, -1.565, -1.565, -1.331, -1.331, -1.331, -1.245, -1.245, -1.245, -1.245, -0.733, -0.733, -0.733, -0.733, -0.733, -0.733, -0.968, -0.968, -0.968, -0.968, -0.477,  -0.477, -0.477, -0.477, 0.377, 0.377, 0.377, 0.377, -0.156, -0.156, -0.156, -0.562, -0.562, -0.562, -0.562, -0.562),

 RM=c(0.694, 0.380, 1.937, 1.556, 1.859, 0.398, -0.453, -0.127, -1.229, -0.469, 0.291, -0.459, -0.704, -0.581, -0.282, -0.816, -0.610, -0.498, -1.586, -1.034, -1.354, -0.549, -0.188, -0.859, -0.632, -1.295, -0.859, -0.382, 0.531, 0.896, -1.062, -0.331, -0.579, -1.087, -0.282, -0.614, -0.802, -0.783, -0.547, 0.735, 1.609, 1.091, -0.133, -0.048, -0.337, -1.125, -0.914, -0.416, -1.702, -1.288, -0.553, -0.243, 0.564, -0.482, -0.706, 2.067, 0.303, 1.185, -0.182, -0.626, -1.005, -0.547, 0.451, 1.075, 1.772, 0.113, -0.912, -0.726, -1.305, -0.712, 0.372, -0.557, -0.345, 0.022, 0.079, 0.105, 0.091, -0.192, -0.005, -0.734, 1.004, 0.784, 0.138, -0.137, 0.315, 0.806, -0.447, -0.231, 1.574, 1.721, 0.372, 0.348, 0.423, -0.048, 0.030, 0.796, -0.145, 3.738, 3.230, 2.407),

 TAX=c(0.142, -1.034, -1.034, -1.470, -1.470, -1.470, 0.468, 0.468, 0.468, 0.468, 0.468, 0.468, 0.468, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, 0.381, -0.228, -0.228, -0.228, -0.228, -0.816, -0.816, -1.230, -1.230, -1.230, -1.230, -1.230, -1.230, -1.230, -1.230, -1.230, -1.012, -1.012, -1.012, -1.012, 3.909, -1.383, 0.512, -0.729, -0.120, -0.120, -0.120, -0.120, -0.120, -0.120, -1.600, 1.035, 1.035, 1.209, 1.209, 1.209, 0.338, 0.338, 0.338, 0.338, 2.363, 2.363, 2.363, 2.363, 2.363, 2.363, -0.185, -0.185, -0.185, -0.185, -0.925, -0.925, -0.925, -0.925, -0.424, -0.424, -0.424, -0.424, -0.424, -0.424, -0.424, -0.294, -0.294, -0.294, -0.294, -0.294),

 PT=c(-1.995, -0.524, -0.524, 0.006, 0.006, 0.006, -2.054, -2.054, -2.054, -2.054, -2.054, -2.054, -2.054, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 1.360, 0.300, 0.300, 0.300, 0.300, -0.230, -0.230, -0.465, -0.465, -0.465, -0.465, -0.465, -0.465, -0.465, -0.465, -0.465, -1.112, -1.112, -1.112, -1.112, 1.419, -0.465, -0.818, -2.113, 0.594, 0.594, 0.594, 0.594, 0.594, 0.594, -0.053, -1.524, -1.524, 0.124, 0.124, 0.124, 0.300, 0.300, 0.300, 0.300, 0.006, 0.006, 0.006, 0.006, 0.006, 0.006, 0.182, 0.182, 0.182, 0.182, -0.112, -0.112, -0.112, -0.112, -0.524, -0.524, -0.524, -0.524, -0.288, -0.288, -0.288, -0.406, -0.406, -0.406, -0.406, -0.406),

 LSTAT=c(-1.016, -0.286, -1.183, -1.374, -0.955, -0.976, 0.291, 1.470, 3.361, 1.110, 1.698, 0.438, 0.866, -0.441, -0.090, -0.404, -0.736, 0.684, 0.161, 0.089, 1.798, 0.536, 1.394, 1.598, 0.970, 1.007, 0.708, 1.142, 0.356, 0.212, 2.075, 0.398, 2.971, 1.329, 1.678, -0.192, 0.112, -0.351, -0.113, -1.132, -1.543, -1.041, -0.871, -0.585, -0.215, -0.099, 0.592, 1.408, 3.515, 0.952, 0.470, -0.236, -0.964, -0.411, 0.707, -1.046, -0.878, -1.197, -0.686, -0.272, 0.417, 0.643, -0.709, -0.223, -0.478, -1.071, -0.093, -0.469, 0.407, -0.348, -0.711, -0.157, -0.922, -0.567, -0.701, -0.322, 0.210, -0.088, 0.275, -0.293, -0.962, -0.623, -0.711, -0.572, -0.202, -0.744, 0.366, -0.409, -0.925, -0.890, -0.344, -0.451, -0.458, -0.801, -0.032, -0.723, 0.099, -1.151, -1.264, -0.804)
)