1. (Y. Itoh, M.A.Papa,B.Krishnan-AEI, X. Siemens –UWM
Chi-square test on candidate events from CW signals coherent searches
(Y. Itoh, M.A.Papa,B.Krishnan-AEI, X. Siemens –UWM
A large value of the detection statistic indicates a candidate signal at the frequency and the sky position
E.g., ~100 outliers of F(f) found in Hz.
True signals produce characteristic line shapes in F=F(f).
Use the F(f) shape information to veto the outliers.
Left figure: Outlier example
Blue line: F(f) computed from LHO 10 h S2 real data targeting at
Red line: Reconstructed veto signal based on the maximum likelihood estimates of the signal parameters.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

2. Yousuke Itoh AEI @ GWDAW8 UW Milwaukee USA 17-20 December 2003
Basic Idea(1)
The detection statistic: Jaranowski et al. Phys.Rev.D58:063001,1998
If the data=random Gaussian noise (r.g.n)
 ( distribution)
If data=r.g.n + signal 
(Non-cent with Non-cent. param.= SNR)
Hypothesis: data=rand. Gaussian noise + signal
becomes the χ^2 dist. if our reconstruction of the signal is good!
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

3. Yousuke Itoh AEI @ GWDAW8 UW Milwaukee USA 17-20 December 2003
Basic Idea (2)
Use the maximum likelihood estimates of the signal parameters.
instead of unknown
Use the targeting sky position
instead of unknown signal sky position
If the veto statistic is extremely large, we veto out the outlier.
Need to be careful
SNR dependent threshold on the veto statistic.
(Cf. TAMA inspiral upper limit report)
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

4. Yousuke Itoh AEI @ GWDAW8 UW Milwaukee USA 17-20 December 2003
Safety test
False dismissal
Procedure
Inject ~ 10^6 fake signals with randomly chosen signal params and signal sky positions into 10 h Gaussian stationary noise.
Compute (~SNR) and the veto statistic for each outlier. Targeting sky position satisfies
The red line gives 0 % false dismissal for this experiment.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

5. Yousuke Itoh AEI @ GWDAW8 UW Milwaukee USA 17-20 December 2003
Efficiency test
False alarm
Procedure
Inject ~ 10^6 damped line noises with randomly chosen params into 10 h Gaussian stationary noise.
Compute (~SNR) and the veto statistic for each outlier. Targeting sky position satisfies
The red line gives 8 % false alarm for this experiment.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

6. Application to Real data
Procedure
Apply the veto method on 10 h LHO4K S2 real data starting from GPS time
Compute (~SNR) and the veto statistic for each outlier.
1200 targeting sky positions are randomly chosen.
Frequency band is Hz.
465.7 Hz line
16 Hz multiples
The red line vetos 69 % of the outliers found in this data.
Some of the “Arms” are due to lines with particular freqs.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

7. Preliminary! Application to Real data
With the line noise table provided by
R. Berkowitz, M. Landry, D. Ottaway, R. Schofield
Preliminary!
Procedure (yet to be examined!)
Remove 16 Hz multiples (+-1Hz).
Remove the measured lines between Hz.
465.7 Hz line
16 Hz multiples
Experimentalists veto out some of the arms most efficiently!
The red line now vetos 75 % of the outliers found in this data.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

8. Remarks and Conclusion
Our veto method is rather efficient: Even with rough parameters tuning, it is demonstrated for some real data that adopting some threshold on our veto statistic, ~ 69 % of the outliers can be vetoed out. Safety test shows that the same threshold on the veto statistic gives effectively 0% (modulo sample variance) false dismissal rate.
We have performed the safety and efficiency tests on the real data and obtained similar results.
There are still outliers that we might keep. While studying parameters tuning and making the method more efficient, we study other veto methods and use combinations of various veto methods.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

9. Veto the outliers in FDS
Other possible veto strategies not yet studied.
(a) Coincidence among other channels:
F stat. outliers  characteristic line noises of the instruments. Coincidence analysis among h(t) and other channels. Needs Veto channels selection.
(b) Follow up:
If true signal, the amplitude of F stat. varies w.r.t. time in a predictable maner (= Doppler amp./phase mod. etc.). Search the signal in the other IFOs, time periods, etc.
(c) Coincidence among the IFOs.
Consistency check on the MLEs of the strain that the IFOs give us.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

10. Yousuke Itoh AEI @ GWDAW8 UW Milwaukee USA 17-20 December 2003
465.7 Hz line
Tuning the Veto method
Left figure: Hz line in F(f)
Blue line: F(f) computed from LHO 10 h S2 real data targeting at
Red line: Reconstructed veto signal based on the maximum likelihood estimates of the signal parameters.
Method and parameter tuning are being studied.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

11. Convergence of the probability at given SNR
Histogram
Convergence of the probability at given SNR
Normalized histogram as a function of the veto statistic for some selected ranges of SNR.
Efficiency test
Safety test
Pdf is well estimated. Sample size in each class is ~ 10^4-5.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003

12. Maximum Likelihood Estimates of the Signal Parameters.
Left figure: Goodness of the estimates
Goodness of the Maximum likelihood estimates of the four amplitudes.
Injected signals are the same as those in the safety test. Thus, ~10^6 fake signals injected into 10 h stationary Gaussian random noise.
Signal parameters are well estimated.
Yousuke Itoh GWDAW8 UW Milwaukee USA December 2003