Analytic score distributions for a spatially continuous tridirectional Monte Carol transport problem

The interpretation of the statistical error estimates produced by Monte Carlo transport codes is still somewhat of an art. Empirically, there are variance reduction techniques whose error estimates are almost always reliable, and there are variance reduction techniques whose error estimates are often unreliable. Unreliable error estimates usually result from inadequate large-score sampling from the score distribution's tail. Statisticians believe that more accurate confidence interval statements are possible if the general nature of the score distribution can be characterized. Here, the analytic score distribution for the exponential transform applied to a simple, spatially continuous Monte Carlo transport problem is provided. Anisotropic scattering and implicit capture are included in the theory. In large part, the analytic score distributions that are derived provide the basis for the ten new statistical quality checks in MCNP