Feldman-Cousins Analysis at CMS
Advisor(s)
Dr. Peter Dong, Illinois Mathematics and Science Academy
Location
Room A149
Start Date
26-4-2019 11:05 AM
End Date
26-4-2019 11:20 AM
Abstract
Feldman and Cousins introduced a statistical technique to perform a frequentist analysis which unifies upper and lower limits with two-sided confidence intervals. This solves the problem that the choice of upper limit or two-sided interval leads to intervals that do not give frequentist coverage if the choice is dependent on the data. The Feldman-Cousins approach involves sorting pseudoexperiments by their likelihood ratio, or R value. This involves sorting a number of points in N-dimensional space by their R values. After removing the points with the lowest likelihood, the remaining points define a region in space: a simple task in the single-channel case, but a more difficult one in the general N-channel case. An algorithm must be employed to determine whether a given pseudoexperiment is contained in the defined region. The current "box" approximation on a sample dataset yielded a lower limit of 15.47 TeV, compared to the Bayesian limit of 21.14 TeV. Work is underway on a multi-dimensional hull algorithm, a more aggressive approximation which will raise this limit even further.
Feldman-Cousins Analysis at CMS
Room A149
Feldman and Cousins introduced a statistical technique to perform a frequentist analysis which unifies upper and lower limits with two-sided confidence intervals. This solves the problem that the choice of upper limit or two-sided interval leads to intervals that do not give frequentist coverage if the choice is dependent on the data. The Feldman-Cousins approach involves sorting pseudoexperiments by their likelihood ratio, or R value. This involves sorting a number of points in N-dimensional space by their R values. After removing the points with the lowest likelihood, the remaining points define a region in space: a simple task in the single-channel case, but a more difficult one in the general N-channel case. An algorithm must be employed to determine whether a given pseudoexperiment is contained in the defined region. The current "box" approximation on a sample dataset yielded a lower limit of 15.47 TeV, compared to the Bayesian limit of 21.14 TeV. Work is underway on a multi-dimensional hull algorithm, a more aggressive approximation which will raise this limit even further.