This research will develop new techniques to characterize spatial clustering in large astronomical datasets. The principal goal is a new edge-corrected, banded bispectrum estimator based on a unique combination of ideas: i) carefully analyze and fully exploit the underlying symmetries, ii) correct for symmetry breaking by the window and noise in pixel space, iii) use edge corrected, nearly optimal estimators with heuristic weighting, iv) use fast, hierarchical computing algorithms v) use regularized, hierarchical (multi-resolution) transform techniques to recover the optimal statistics from pixel space estimators. This unusually broad synergy of mathematics, statistics, computer science, and astronomy will result in a quantum leap in speed and ability to map the full configuration space of spatial clustering. The resultant techniques are practical and applicable to other statistics and to many different large data sets. Results will feed back into a new advanced statistics class, and will be broadly disseminated.
