where n λ is the number of uncorrelated samples obtained at λ, σ 2 ∂H ∂λ λ is the variance of the mean gradient of the Hamiltonian with respect to λ, σ 2 ∂H ∂λ is the variance of the gradient of the Hamiltonian with respect to λ, g λ = t λ n λ is the statistical inefficiency at λ, and t λ is the sampling time at λ. Defining the fractional sampling time as π λ = t λ t Tot. , where t Tot. is the total sampling time for the transformation, yields,