This thesis addresses the long-standing problem in the Inertial Confinement Fusion (ICF) of generating accurate predictions of ICF experiment in order to drive iterative design and optimization. Maximizing the performance of ICF experiments is necessary to achieve the goal of harnessing nuclear fusion for energy generation. The efficient design of high performance experiments has long been obstructed by the lack of accurate predictive models, due in large part to the complex, nonlinear, multi-scale physics involved in a laser fusion experiment. The alternative, statistical approach described here was used to design, quantitatively predict, and interpret the results of implosions of cryogenic deuterium–tritium lined spherical targets on the OMEGA laser system. leading to a tripling of the fusion yield to its highest value so far for direct-drive laser fusion. It has also helped form several hypotheses regarding degradation sources, some of which were tested, validated, and used to improve performance on OMEGA.  This approach could guide the exploration of the vast parameter space of thermonuclear ignition conditions and enhance our understanding of laser-fusion physics.