  A method for determining the $q^2$ dependent $\bar{K}^{*0}$ spin amplitudes
of $\bar{B}^{0}\to \bar{K}^{*0}\mu^+\mu^-$ decays through a maximum likelihood
fit to data is presented. While current experimental techniques extract a
limited set of observables in bins of $q^2$, our approach allows for the
determination of all observable quantities as continuous distributions in
$q^2$. By doing this, the method eliminates the need to correct theory
predictions of these observables for $q^2$ averaging effects, thus increasing
the sensitivity to the effects of physics beyond the Standard Model. Accounting
for the symmetries of the angular distribution and using a three parameter
ansatz for the $q^2$ dependence of the amplitudes, the precision of the angular
observables and the sensitivity to new physics is estimated using simulated
events. These studies are based on the sample sizes collected by the LHCb
experiment during Run-I and expected for Run-II.
