  Recent experiments have reached detection efficiencies sufficient to close
the detection loophole, testing the Clauser-Horne (CH) version of Bell's
inequality. For a similar future experiment to be completely loophole-free, it
will be important to have discrete experimental trials with randomized
measurement settings for each trial, and the statistical analysis should not
overlook the possibility of a local state varying over time with possible
dependence on earlier trials (the "memory loophole"). In this paper, a
mathematical model for such a CH experiment is presented, and a method for
statistical analysis that is robust to memory effects is introduced.
Additionally, a new method for calculating exact p-values for martingale-based
statistics is described; previously, only non-sharp upper bounds derived from
the Azuma-Hoeffding inequality have been available for such statistics. This
improvement decreases the required number of experimental trials to demonstrate
non-locality. The statistical techniques are applied to the data of recent
experiments and found to perform well.
