I think you really might want to take some time to go through the documentation and learn some of the basics of Julia, a good starting point might be http://julia.readthedocs.org/en/latest/manual/noteworthy-differences/
The first error is simply telling you that the result of *broadcast(*,Pr,GI[:,1,:]) *has dimension 4x3x3, while *F[:,1,:] *is an array of dimension 4x1x3. The second error says that you can't multiply a 4x1x3 array, while the third error says that you can't do this elementwise, either. The main problem seems to be that (e.g.) G.I[,1,] produces a 4x3 matrix in R, while GI[:,1,:] returns a 4x1x3 array in Julia. You need to make sure that the indexing you're using in Julia is actually returning the objects you're expecting. You should have a look at the reshape() and the squeeze() functions (e.g. in your second error, GI[:,2,:].*(squeeze(F[:,2-1,:],2)*Tr) would wok, although I'm not entirely sure that's what you're trying to achieve!
