We first review the requirements of Monte Carlo neutron transport codes to accurately model the phenomena associated with the unresolved resonance regime and present the first rigorous justification for the modeling assumption employed by probability tables for unresolved resonances. We present a new method named AURA (analytic unresolved resonance algorithm) for modeling unresolved resonance cross-sections with the normal inverse Gaussian distribution. The new method accurately models temperature dependence in the unresolved resonance region (URR), requires fewer data than previous methods, and outperforms the conventional URR treatment on GPUs.