Searching for sources of the highest energy cosmic rays: low statistics, pitfalls, and possible clues

The clustering properties of the highest energy cosmic rays and their correlations with candidate sources are re-examined using the most recently available AGASA data and a rigorous correlation analysis. The statistical methodology incorporates some important points not considered in previous studies. Results include small angle clustering significances consistent with, but somewhat less than, earlier findings, a possible large scale anisotropy for events with energies $E\approx 5-8\times {10}^{19}\mathrm{e}\mathrm{V}$, and no statistically significant cross correlations with BL Lacertae or blazars. A marginally significant cross correlation exists for events with energies $E > 8 \times 10^{19} $\mathrm{e}\mathrm{V}$$ with a set of Abell clusters, but no definitive conclusion can yet be drawn from this result.