  In this paper, we consider a backward in time problem for Ginzburg-Landau
equation in multidimensional domain associated with some random data. The
problem is ill-posed in the sense of Hadamard. To regularize the instable
solution, we develop a new regularized method combined with statistical
approach to solve this problem. We prove a upper bound, on the rate of
convergence of the mean integrated squared error in $L^2 $ norm and $H^1$ norm.
