Dear WinBUGs-Community,
I'm trying to fit a finite mixture of two bivariate normal distributions with unknown means and unknown variances.
Therefore, I generated 400 cases which represent the mixture distribution.
The first 200 cases were sampled from a bivariate normal distribution with the mean vector (0,0) and the 2x2-covariance matrix (1, .3, .3, 1). This means that the first 200 cases were sampled from a bivariate standard normal distribution with a correlation of .3.
The second 200 cases were sampled from a bivariate normal distribution with the mean vector (1,2) and the 2x2-covariance matrix (4,2,2,4).
The complete dataset (400 cases) was created by appending the second 200 cases to the first 200 cases.
Now, I would like to analyze this complete dataset. I specified a model and WinBUGs says that it is syntactically correct. After loading the dataset and trying to compile the code, there is an error message: "multivariate node expected".
Does anybody know what could be wrong? Attachted you will find the model syntax and the data set. Unfortunately, the Bugs-examples were not so helpful.
Thank you very much for your help.
Best,
Mene
###############
model
{
for( i in 1 : N ) {
y[i,1] <- X[i,1]
y[i,2] <- X[i,2]
y[i,1:2] ~ dmnorm(mu[i,1:2], tau[i,1:2,1:2])
mu[i,1:2] <- lambda[T[i],1:2]
tau[i,1:2,1:2] <- prec[T[i],1:2,1:2]
T[i] ~ dcat(P[1:2])
}
P[1:2] ~ ddirch(alpha[1:2])
prec[1,1:2,1:2]~dwish(PHinv[1:2,1:2],4)
prec[2,1:2,1:2]~dwish(PHinv[1:2,1:2],4)
prec2[1,1:2,1:2]<-prec[1,1:2,1:2]*N
prec2[2,1:2,1:2]<-prec[2,1:2,1:2]*N
theta[1:2] ~ dmnorm(beta[1:2],prec2[2,1:2,1:2])I(beta[1:2], )
lambda[1,1:2] ~ dmnorm(beta[1:2],prec2[1,1:2,1:2])
lambda[2,1:2] <- lambda[1,1:2] + theta[1:2]
}
###############
###############
list(N = 400, beta = c(0,0), PHinv = structure(.Data = c(1.0, 0.5, 0.5, 1.0), .Dim = c(2, 2)),
alpha = c(1,1),
X = structure(
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T = c(1, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, !
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2)
)
###############
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