On the optimization of Monte-Carlo simulations

The optimal planning of Monte-Carlo simulations is studied. It is assumed that (i) the aim of the simulations is to calculate the value of a certain parameter of a model function as accurately as possible; (ii) the simulations are performed at different values of the control parameter L; (iii) the parameters of the model function are calculated by the means of least-square fit. It is shown that the standard deviation of the outcome achieves minimum when the number of test points (i.e. different values of the parameter L used in simulations) equals the number n of unknown parameters in the model function.