The moving block bootstrap to assess the accuracy of statistical estimates in Ising model simulations Original Research Article

The moving block bootstrap is a resampling method for assigning measures of accuracy to statistical estimates when the observations are in the form of finite time series of correlated data. The method does not require special assumptions and/or intermediate computations of other quantities. It consists in drawing blocks of fixed length randomly with replacement from among the blocks of measured data, and joining them. This paper shows how the moving block bootstrap can be applied successfully to a simple cubic spin flip Ising model, to assess standard errors and confidence intervals for thermodinamics densities (magnetization and magnetization squared per spin) and response functions (magnetic susceptibility), at temperatures both greater than and equal to the critical temperature. In the latter situation, where the correlation function has a slow decay in time, we find (rising internal consistency) that the moving block bootstrap works better than other methods based on subseries values, as for instance a renormalization group method, known as “blocking method”.