In analogy with the Variational Monte Carlo approach and following the Monte Carlo method for evaluating integrals, we can interpret | Ψ Ψ ( X , t ) | 2 ∫ ∫ | Ψ Ψ ( X , t ) | 2 d X as a probability distribution function over the multi-dimensional space spanned by the many-body configurations X . The Metropolis–Hastings algorithm is then used to sample exactly from this probability distribution and, at each time t , the quantities entering the equation of motion are evaluated as statistical averages over the sampled configurations. The trajectories a ( t ) of the variational parameters are then found upon numerical integration of the associated differential equation.