Jin Huang M.I.T. For Transversity Collaboration Meeting Jan 29, JLab Overview Goals, Focuses Comparison of MLE Application of MLE in Transversity Yield Calculation Asymmetry Estimation Angular Modulation Estimation Discussion Asymmetry Cross Check SSA HRS/BigBite Single DSA HRS Single DSA Overview Summary and TODOs Transversity Collaboration Meeting Jin Huang 2 Goals, Focuses Comparison of MLE Transversity Collaboration Meeting Jin Huang 3 Knowing total charge and DAQ/electronics life time of each spin state target/beam polarization, density and luminosity for each event, physics event type, which spin/helicity state its from and related kinematics variables Wanted: angular modulations Transversity Collaboration Meeting Jin Huang 4 Maximum likelihood Estimation (MLE) is a popular statistical method providing estimates for the models parameters At large total event numbers, MEL is asymptotically unbiased its bias tends to zero as the sample size increases asymptotically efficient no asymptotically unbiased estimator has lower asymptotic mean squared error than the MLE. Transversity Collaboration Meeting Jin Huang 5 Cross check with existing methods Do not require binning for angular modulation estimation Use all angular information since do not bin data bin data = assume all data coming from bin center or loosing angle information O(bin size/2) Possible to 1 st order canceling by using weighted center More stable if statistics is low Fitting method require statistics is high in each bin, or Poisson Distribution is near Gaussian. Eg. It will fail if average bin count