#### Event Title

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.