Astronomers study large-scale structure, usually with second-order statistics of clustering, in order to understand the Universe and its evolution. To get error estimates, bootstrap is often used. This project will extend recently developed methods that dramatically reduce standard errors by considering the dependence of absorbers across different radial lines of observation, and will apply these techniques to a new larger dataset. The research work will also compare different measures of second-order structure in spatial point processes, and study methods of resampling spatial data. Extending the method to variable size absorbers, chemical element differences, and third-order characteristics, should provide clustering estimates of unprecedented precision. Analysis of surveys and simulations using various estimators should improve understanding of the procedures, and provide recommendations of appropriate measures for different situations. Resampling spatial processes is complicated and computationally intensive, and a new faster method will be tested on real data and simulations using both simple regions and more realistic, more complex regions. This work will advance statistical understanding of both theoretical and applied issues involved in estimating clustering and resampling spatial data.
All of these results will be important for applied statistical work in many fields, and will be disseminated as widely as possible to the statistics and astronomy communities. The research also involves significant interdisciplinary collaboration and training, including members of under-represented groups.
