[精彩WinBUGS答问]How to get prediction for a specific variable in WinBUGS?

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I am a new user of WinBUGS and have one question for your help. After running the following code, I got parameters of beta0 through beta4 (stats, density), but I don't know how to get the prediction of the last value of h, which I set to NA to model in the code.

Does anyone can given me a hint? Any advice would be greatly appreciated.

model {
for(i in 1: N) {
CF01 ~ dnorm(0, 20)
CF02  ~ dnorm(0, 1)
h ~ dpois (lambda )
log(lambda ) <- beta0 + beta1*CF03 + beta2*CF02 + beta3*CF01 + beta4*IND
}
beta0 ~ dnorm(0.0, 1.0E-6)
beta1 ~ dnorm(0.0, 1.0E-6)
beta2 ~ dnorm(0.0, 1.0E-6)
beta3 ~ dnorm(0.0, 1.0E-6)
beta4  <- log(p)
p ~ dunif(lower, upper)
}

INITS
list(beta0 = 0, beta1 = 0, beta2 = 0, beta3 = 0, p = 0.9)

DATA(LIST)
list(N = 154, lower = 0.80, upper = 0.95,

h = c(1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 3, 0, 0, 0, 2, 0, 1, 0, 4, 2,
3, 0, 2, 1, 1, 2, 2, 2, 3, 4, 2, 3, 1, 0, 1, 3, 3, 3, 1, 0, 1,
0, 5, 2, 1, 2, 1, 3, 3, 1, 1, 0, 2, 2, 0, 3, 0, 0, 3, 2, 2, 2,
1, 0, 3, 3, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 0, 2, 1, 0, 0, 2, 5,
0, 2, 1, 0, 2, 1, 2, 2, 2, 0, 3, 2, 1, 3, 3, 3, 3, 0, 1, 3, 3,
3, 1, 0, 0, 1, 2, 1, 0, 1, 4, 1, 1, 1, 1, 2, 1, 3, 0, 0, 1, 1,
1, 1, 0, 2, 1, 0, 0, 1, 1, 5, 1, 1, 1, 3, 0, 1, 1, 1, 0, 2, 1,
0, 3, 3, 0, 0, 1, 2, 6, NA),

CF03 = c(-1.575, 0.170, -1.040, -0.010, -0.750,
0.665, -0.250, 0.145, -0.345, -1.915, -1.515,
0.215, -1.040, -0.035, 0.805, -0.860, -1.775,
1.725, -1.345, 1.055, -1.935, -0.160, -0.075,
-1.305, 1.175, 0.130, -1.025, -0.630, 0.065,
-0.665, 0.415, -0.660, -1.145, 0.165, 0.955,
-0.920, 0.250, -0.365, 0.750, 0.045, -2.760,
-0.520, -0.095, 0.700, 0.155, -0.580, -0.970,
-0.685, -0.640, -0.900, -0.250, -1.355, -1.330,
0.440, -1.505, -1.715, -0.330, 1.375, -1.135,
-1.285, 0.605, 0.360, 0.705, 1.380, -2.385, -1.875,
-0.390, 0.770, 1.605, -0.430, -1.120, 1.575, 0.440,
-1.320, -0.540, -1.490, -1.815, -2.395, 0.305,
0.735, -0.790, -1.070, -1.085, -0.540, -0.935,
-0.790, 1.400, 0.310, -1.150, -0.725, -0.150,
-0.640, 2.040, -1.180, -0.235, -0.070, -0.500,
-0.750, -1.450, -0.235, -1.635, -0.460, -1.855,
-0.925, 0.075, 2.900, -0.820, -0.170, -0.355,
-0.170, 0.595, 0.655, 0.070, 0.330, 0.395, 1.165,
0.750, -0.275, -0.700, 0.880, -0.970, 1.155, 0.600,
-0.075, -1.120, 1.480, -1.255, 0.255, 0.725,
-1.230, -0.760, -0.380, -0.015, -1.005, -1.605,
0.435, -0.695, -1.995, 0.315, -0.385, -0.175,
-0.470, -1.215, 0.780, -1.860, -0.035, -2.700,
-1.055, 1.210, 0.600, -0.710, 0.425, 0.155, -0.525,
-0.565),

CF02 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, 0.38, 0.06, -0.94,
-0.02, -0.28, -0.78, -0.95, 2.33, 1.43, 1.24, 1.26,
-0.75, -1.5, -2.09, 1.01, -0.05, 2.48, 2.48, 0.46,
0.46, -0.2, -1.11, 0.52, -0.37, 0.58, 0.86, 0.59,
-0.12, -1.33, 1.4, -1.84, -1.4, -0.76, -0.23,
-1.78, -1.43, 1.2, 0.32, 1.87, 0.43, -1.71, -0.54,
-1.25, -1.01, -1.98, 0.52, -1.07, -0.44, -0.24,
-1.31, -2.14, -0.43, 2.47, -0.09, -1.32, -0.3,
-0.99, 1.1, 0.41, 1.01, -0.19, 0.45, -0.07, -1.41,
0.87, 0.68, 1.61, 0.36, -1.06, -0.44, -0.16, 0.72,
-0.69, -0.94, 0.11, 1.25, 0.33, -0.05, 0.87, -0.37,
-0.2, -2.22, 0.26, -0.53, -1.59, 0.04, 0.16, -2.66,
-0.21, -0.92, 0.25, -1.36, -1.62, 0.61, -0.2, 0,
1.14, 0.27, -0.64, 2.29, -0.56, -0.59, 0.44, -0.05,
0.56, 0.71, 0.32, -0.38, 0.01, -1.62, 1.74, 0.27, 0.97,
1.22, -0.21, -0.05, 1.15, 1.49, -0.15, 0.05, -0.87,
-0.3, -0.08, 0.5, 0.84, -1.67, 0.69, 0.47, 0.44,
-1.35, -0.24, -1.5, -1.32, -0.08, 0.76, -0.57,
-0.84, -1.11, 1.94, -0.68),

CF01 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, -0.117, -0.211, -0.333, -0.229, -0.272,
-0.243, -0.148, 0.191, -0.263, -0.239, -0.168,
-0.381, -0.512, -0.338, -0.296, 0.067, 0.104,
-0.254, -0.167, -0.526, -0.096, -0.43, 0.013,
-0.438, -0.297, -0.131, -0.098, -0.046, -0.063,
-0.194, -0.155, -0.645, -0.603, -0.374, -0.214,
-0.165, -0.509, -0.171, -0.442, -0.468, -0.289,
-0.427, -0.519, -0.454, 0.046, -0.275, -0.401,
-0.542, -0.488, -0.52, -0.018, -0.551, -0.444,
-0.254, -0.286, 0.048, -0.03, -0.015, -0.219,
-0.029, 0.059, 0.007, 0.157, 0.141, -0.035, 0.136,
0.526, 0.113, 0.22, -0.022, -0.173, 0.021, -0.027,
0.261, 0.082, -0.266, -0.284, -0.097, 0.097, -0.06,
0.397, 0.315, 0.302, -0.026, 0.268, -0.111, 0.084,
0.14, -0.073, 0.287, 0.061, 0.035, -0.022, -0.091,
-0.22, -0.021, -0.17, -0.184, 0.121, -0.192,
-0.24, -0.283, -0.003, -0.45, -0.138, -0.143,
0.017, -0.245, 0.003, 0.108, 0.015, -0.219, 0.09,
-0.22, -0.004, -0.178, 0.396, 0.204, 0.342, 0.079,
-0.034, -0.122, -0.24, -0.125, 0.382, 0.072, 0.294,
0.577, 0.4, 0.213, 0.359, 0.074, 0.388, 0.253, 0.167),

IND = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 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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关键词：Prediction Specific Variable winbugs predict prediction following specific question running

ust add the variable h to the list of the parameters to be monitored. If you are using package like R2WinBUGS, then add variable h to to the list passed to parameters.to.save argument to the bugs function. Then look at your last value in h (the one with NA) - you will get a posterior distribution there.

This is usual way to make predictions in bayesian inference (see also this question). It is nice and simple! No more separation of parameter evaluation and prediction. Everything is done at once. The posterior distrubution of parameters is given by the actual data and propagated to the NA values (as "predictions").

As far as I can tell, the lambdas are exactly what one wants to predict: this is a generalized linear model for a Poisson distribution with log link and the lambdas are the predicted Poisson parameters. They have not been observed. I believe all one needs to do here is to set a monitor on lambda[N].