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A study of compatibility

A study of compatibility. N c 2 c 2 /N. Table of Data Sets. The PDF’s are not exactly CTEQ6 but very close – a no-name generic set of PDF’s for illustration purposes. N tot = 2291 c 2 global = 2368. The effect of setting all normalization constants to 1. Dc 2.

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A study of compatibility

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  1. A study of compatibility PHYSTAT 2003

  2. N c2 c2/N Table of Data Sets The PDF’s are not exactly CTEQ6 but very close – a no-name generic set of PDF’s for illustration purposes. Ntot = 2291 c2global= 2368. PHYSTAT 2003

  3. The effect of setting all normalization constants to 1. Dc2 c2(opt. norm) = 2368. c2(norm 1) = 2742. Dc2 = 374.0 PHYSTAT 2003

  4. By applying weighting factors in the fitting function, we can test the “compatibility” of disparate data sets. Example 1. The effect of giving the CCFR F2 data set a heavy weight. Dc2 Dc2 (CCFR) = -19.7 Dc2 (other) = +63.3 Giving a single data set a large weight is tantamount to determining the PDF’s from that data set alone. The result is asignificant improvement for that data set but which does not fit the others. PHYSTAT 2003

  5. Example 1b. The effect of giving the CCFR F2 data weight 0, i.e., removing the data set from the global analysis. Dc2 Dc2(CCFR) = +40.0 Dc2 (other) = -17.4 Imagine starting with the other data sets, not including CCFR. The result of adding CCFR is that c2global of the other sets increases by 17.4 ; this must be an acceptable increase of c2 . PHYSTAT 2003

  6. Example 2. ZEUS F2 measurements (Like fitting ZEUS alone) Heavy weight for ZEUS Dc2(zeus) = -13.7 Dc2 (other) = +64.6 Zero weight for ZEUS Dc2(zeus) = +18.3 Dc2(other) = -10.6 [removing zeus => c2 (other) decreases by 10.6] PHYSTAT 2003

  7. Example 3. H1 data sets Heavy weight for H1 data Dc2 Dc2 (H1) = -27.2 Dc2 (other) = +106.1 Zero weight for H1 Dc2 Dc2 (H1) = +18.1 Dc2 (other) = -11.0 PHYSTAT 2003

  8. Example 4. The D0 jet cross section Heavy weight for D0 jet Dc2 (D0 jet) = -7.8 Dc2 (other) = +26.8 Zero weight for D0 jet Dc2 (D0 jet) = +64.3 Dc2 (other) = -6.5 PHYSTAT 2003

  9. Example 5. Giving heavy weight to H1 and BCDMS Dc2 Dc2 for all data sets Dc2(H & B) = -38.7 Dc2(other) = +149.9 PHYSTAT 2003

  10. Lessons from these reweighting studies • Global analysis requires compromises – the PDF model that gives the best fit to one set of data does not give the best fit to others. This is not surprising because there are systematic differences between the experiments. • The scale of acceptable changes of c2 must be large. Adding a new data set and refitting may increase the c2‘s of other data sets by amounts >> 1. PHYSTAT 2003

  11. Clever ways to test the compatibility of disparate data sets • Plot c2 versus c2 J Collins and J Pumplin (hep-ph/0201195) • The Bootstrap Method Efron and Tibshirani, Introduction to the Bootstrap (Chapman&Hall) Chernick, Bootstrap Methods (Wiley) PHYSTAT 2003

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