Molecular dynamics (MD) is an important method underlying the modern field of Computational Materials Science. Without requiring prior knowledge as inputs, MD simulations have been used to study a variety of material problems. However, results of molecular dynamics simulations are often associated with errors as compared with experimental observations. These errors come from a variety of sources, including inaccuracy of interatomic potentials, short length and time scales, idealized problem description and statistical uncertainties of MD simulations themselves. This chapter specifically devotes to the statistical uncertainties of MD simulations. In particular, methods to quantify and reduce such statistical uncertainties are demonstrated using a variety of exemplar cases, including calculations of finite temperature static properties such as lattice constants, cohesive energies, elastic constants, dislocation energies, thermal conductivities, surface segregation and calculations of kinetic properties such as diffusion parameters. We also demonstrate that when the statistical uncertainties are reduced to near zero, MD can be used to validate and improve widely used theories
