Multivariate random walks in BUGS

Question

I want to jointly estimate a very simple MV-Normal two-dimensional AR[1] process, $[x_t,y_t]=[x_{t-1},y_{t-1}]+\text{[Bivariate Gaussian error]}$, in BUGS. But the syntax has been impossible to figure out. Here's the problem part of the code:

 ## transition model (aka random walk prior)
 for(i in 2:NPERIODS1){         
    mu.vector[i,1:2]<-vector[i-1,1:2]
    vector[i,1:2]~dmnorm(mu.vector[i,1:2], omega[1:2,1:2])
    }

The compiler throws up a "Expected a multivariate node" error. Looking through some examples, there doesn't seem to be any easy way to introduce a structured mean or covariance variables for the multivariate normal function. How should I proceed?

Edit: Changed omega[,] to omega[1:2,1:2] for clarity.

Answer 1

Have you tried replacing omega[,] with omega[1:2,1:2]? I haven't got BUGS here but IIRC that's what it expects inside dmnorm.

Answer 2

Even though this is over a year late, for posterity I think it should be answered since I stumbled onto this thread with essentially the same question. The problem is that in BUGS the <- assignment operator is only defined on scalars. So, the appropriate code is

## transition model (aka random walk prior)
for(i in 2:NPERIODS1){   
    for(j in 1:2){      
        mu.vector[i,j]<-vector[i-1,j]
    }
    vector[i,1:2]~dmnorm(mu.vector[i,1:2], omega[1:2,1:2])
}

I'm not entirely sure why it doesn't give a model-check error, so maybe there is a valid way to use <- with vectors/matricies/arrays, but not here at any rate.

Answer 3

I disagree with @guy since the "<-" assignment works for matrices.

I think you have to "fill" the matrix mu.vector starting from the first line, you cannot start from the second line. Then type :

 for(i in 2:NPERIODS1){         
    mu.vector[i-1,1:2]<-vector[i-1,1:2]
    vector[i,1:2]~dmnorm(mu.vector[i-1,1:2], omega[1:2,1:2])
    }

I'm not sure because I haven't used WinBUGS since a couple of years. Another possibility is that it does not allow operations on the indices inside the brackets "[...]". If that holds true, then define a vector j such that j[i]=i-1 and type

   for(i in 2:NPERIODS1){         
        mu.vector[j[i],1:2]<-vector[j[i],1:2]
        vector[i,1:2]~dmnorm(mu.vector[j[i],1:2], omega[1:2,1:2])
        }

By the way your code is incomplete (how is vector[1,] defined ?..). Hence this is difficult to help ! The error is possibly due to wrong dimensions when you load initial values or data.