Project #1 With Richard Lockhart

Goodness-of-fit with weighted data

Physicists are often interested in comparing simulated data to real data to see if the two samples come from the same distribution.  Classically, these comparisons are made by `binning' the data and using Pearson's chi-squared statistic. But there are many reasons for thinking this might not be a very sensitive method of comparison.  In particular, tests based on empirical distribution methods might do better.

The USRA student would have the following responsibilities and be asked to do whichever ones turn out to be most practical:

1. Review of the statistics literature for weighted tests of fit -- one sample and two sample.
2. Review of the physics literature for real examples of methods used by physicists.
3. Development of R code for both chi-squared and empirical distribution tests and then general code for doing Monte Carlo studies of performance.
4. Evaluation of the properties of the various tests in realistic (as determined from the physics literature review) situations.
5. Working with the supervisor to describe the theoretical properties of these procedures.