1. 1 Approaching the Problem of Statistics David Forrest University of Glasgow CM23 HIT, Harbin January 14th

2. 2 The Problem - We don't know the statistical error on the measurement we want to make in the MICE - But our aim is to show 10% emittance drop with an error of 1%.... - We need to know the statistical error on the fractional change of emittance

3. 3 Trackers We calculate 4D emittance from the fourth root of a determinant of a matrix of covariances...The problem is compounded because our data is highly correlated between two trackers.

4. 4 How We Mean To Proceed W e assume that we will discover a formula that takes the form Sigma=K*(1/sqrt(N)) where K is some constant or parameter to be determined. How do we determine K? 1) First Principles: do full error propagation of cov matrices → difficult calculation 2) Run a large number of G4MICE simulations, using the Grid, to find the standard deviation for every element in the covariance matrix → Toy Monte Carlo (ready to start this month) 3) Empirical approach: large number of simulations to plot   versus 1/sqrt(N), identifying K (started)

5. 5 Empirical approach For N= 1000 then:   = 0.0074 (with  = -0.210) For N= 10,000 then   = 0.0021(with  = -0.210) 500 1k event runs 50 10k event runs

6. 6 10pi K=0.3115 K=0.31

7. 7 Stats conclusions -Preliminary results suggest that for a 10pi beam the statistical error goes as:   =0.31/sqrt(N) The implication of this is that to achieve 0.1% error measurement we need to run ~10 5 events This needs to be redone for all emittances