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Status of the Hough CW search code - Plans for S2 -

Status of the Hough CW search code - Plans for S2 -. A.M. Sintes, B. Krishnan, M.A. Papa Universitat de les Illes Balears, Spain Albert Einstein Institut, Germany. LSC Meeting Hannover, August 2003 LIGO-G030517-00-Z. Outline. The hierarchical Hough search. Pipeline for S2

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Status of the Hough CW search code - Plans for S2 -

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  1. Status of the Hough CW search code- Plans for S2 - A.M. Sintes, B. Krishnan, M.A. Papa Universitat de les Illes Balears, Spain Albert Einstein Institut, Germany LSC Meeting Hannover, August 2003 LIGO-G030517-00-Z

  2. Outline • The hierarchical Hough search. Pipeline for S2 • Statistics of the Hough maps. Frequentist analysis • Code status • Results on simulated & H1 data

  3. The concept of the Hough transform • The idea is to perform a search over the total observation time using an incoherent (sub-optimal) method: We propose to search for evidence of a signal whose frequency is changing over time in precisely the pattern expected for some one of the parameter sets • The method used is the Hough transform f {a,d,f0,fi} t

  4. Coherent search (a,d,fi) in a frequency band raw data GEO/LIGO Incoherent search Peak selection in t-f plane Hough transform(a, d, f0, fi) Hierarchical Hough transform strategy Pre-processing Divide the data set in N chunks Template placing Construct set of short FT (tSFT) Candidates selection Set upper-limit Candidates selection

  5. The time-frequency pattern • SFT data • Demodulated data Time at the SSB for a given sky position

  6. Pre-processing raw data GEO/LIGO Divide the data set in N chunks Incoherent search Peak selection in t-f plane Hough transform(a, d, f0, fi) Incoherent Hough search:Pipeline for S2 Construct set of short FT (tSFT<1800s) Candidates selection Set upper-limit

  7. Peak selection in the t-f plane • Input data: Short Fourier Transforms (SFT) of time series(Time baseline: 1800 sec, calibrated) • For every SFT, select frequency bins i such exceeds some threshold r0  time-frequency plane of zeros and ones • p(r|h, Sn) follows a 2 distribution with 2 degrees of freedom: • The false alarm and detection probabilities for a thresholdr0 are

  8. Hough statistics • After performing the HT using N SFTs, the probability that the pixel {a,d,f0,fi} has a number count n is given by a binomial distribution: • The Hough false alarm and false dismissal probabilities for a threshold n0  Candidates selection

  9. 30% 90% Frequentist Analysis • Perform the Hough transform for a set of points in parameter space l={a,d,f0,fi}S , given the data: HT: S  N l n(l) • Determine the maximum number count n* n* = max (n(l)): lS • Determine the probability distribution p(n|h0) for a range of h0

  10. Frequentist Analysis • Perform the Hough transform for a set of points in parameter space l={a,d,f0,fi}S , given the data: HT: S  N l n(l) • Determine the maximum number count n* n* = max (n(l)): lS • Determine the probability distribution p(n|h0) for a range of h0 • The 95% frequentist upper limit h095% is the value such that for repeated trials with a signal h0 h095%, we would obtain n  n* more than 95% of the time Compute p(n|h0) via Monte Carlo signal injection, using lS, and 0[0,2], [-/4,/4], cos [-1,1].

  11. Code Status • Stand-alone search code in final phase • Test and validation codes (under CVS at AEI) • Hough routines are part of the LAL library:

  12. Code Status II • Auxiliary functions C-LAL compliant (under CVS at AEI to be incorporated into LAL or LALApps): • Read SFT data • Peak Selection (in white & color noise) • Statistical analysis of the Hough maps • Compute <v(t)> • Under development: • Implementation of an automatic handling of noise features. Robust PSD estimator. • Monte Carlo signal injection analysis code. • Condor submission job. • Input search parameter files

  13. Validation code-Signal only case- (f0=500 Hz) • bla

  14. Validation code-Signal only case- (f0=500 Hz)

  15. Signal only case II

  16. Signal only case II

  17. Results on simulated data Statistics of the Hough maps f0~300Hz tobs=60days N=1440 SFTs tSFT=1800s a=0.2231 <n> = Na=321.3074 n=(Na(1-a))=15.7992

  18. Noise only case

  19. Number count probability distribution 1440 SFTs 1991 maps 58x58 pixels

  20. Comparison with a binomial distribution

  21. 95 % Set of upper limit. Frequentist approach. n*=395  =0.295  h095%

  22. H1 Analysis – the SFTs 1887 Calibrated SFT’s H1 TSFT = 1800s, Band : 263-268 Hz 26 SFT, 0.95 or 1.05

  23. H1 Results 264-265 Hz Input: 1861 SFT 0.5x0.5 srad Output: 19811 maps (51x51 sky locations) N=1861 SFTs a=0.2019 Mean number count=373.8130 <n> = Na=375.7294 n=(Na(1-a))=17.3168

  24. n* 95% • h095%~ 5x10-23 ? Very preliminary H1 Results 264-265 Hz“upper limit estimate” Loudest event n*=473 95 % upper limit n*=473  =0.2715

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