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.
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