Testing gravity with $E_G$: mapping theory onto observations
  We present a complete derivation of the observationally motivated definition
of the modified gravity statistic $E_G$. Using this expression, we investigate
how variations to theory and survey parameters may introduce uncertainty in the
general relativistic prediction of $E_G$. We forecast errors on $E_G$ for
measurements using two combinations of upcoming surveys, and find that
theoretical uncertainties may dominate for a futuristic measurement. Finally,
we compute predictions of $E_G$ under modifications to general relativity in
the quasistatic regime, and comment on the pros and cons of using $E_G$ to test
gravity with future surveys.
