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Burst Statistics

Burst Statistics. Jim Linnemann Michigan State University Mar 7, 2004. A Few Updates. Graduate student Aws left Milagro—personal issues Talking with a possible replacement, but beginning student(s) Workshop at MSU on statistical software Feigelson, Beers, R (Luc Tierney), HEP folk

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Burst Statistics

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  1. Burst Statistics Jim Linnemann Michigan State University Mar 7, 2004

  2. A Few Updates • Graduate student Aws left Milagro—personal issues • Talking with a possible replacement, but beginning student(s) • Workshop at MSU on statistical software • Feigelson, Beers, R (Luc Tierney), HEP folk • Feigelson & Babu, Astrostatistics • Relationship of Root and R language (can send summary) • R is used by research statisticians • Future: software repository for Astronomy/HEP • Can now read some Root trees into R • R has: • Plot types Root doesn’t (1-Dim and n-Dim) • But: missing histograms with error bars • Many statistical tests Root doesn’t • Elegant programming language (interactive + macro) • Large repository of procedures CRAN • Very slick download mechanism • Documentation published in books!

  3. Burst Statistics • Brenda asked me to look at circulars and check the probability calculations • Lots of help from Liz, Andy, David

  4. Short Bursts • Purely Poisson calculation by table interpolation • Completely ignores uncertainty in background • Ignore sky motion 48 sec max = .2 degree • b = n(T)  N(t*) / N(T)  t/t* (no bin exclusion) n(T) = in bin during map period (T = ½h, 2h?) N(T) = all sky counts in map t = search period t* = max(10s, t) • Define effective α = (δb)2 / b (like Ton/Toff) • α  (t*/T) + n(T)/N(T)  t*/T + b/Rt + H.O. • Assume Poisson; R = trigger rate is roughly constant • t*/T > .005-.025; b/Rt small correction • α is small, and neglecting it a good approximation

  5. Short Burst StatisticsOct 03 to mid-Feb 04 I performed many checks in Excel and mathematica Spreadsheet to Brenda: histogram declination…

  6. Li Ma 17 • Li Ma 17 includes background uncertainty • But in a Gaussian approximation • Can rewrite as: ½ Z217= x Ln(x/b) + (x+y) Ln r, where x = Non, b = α y y = Noff r = (1 + α) / (1 + αm) = (1 + α) / (1 + x/y) Can with care take limit α  0 Z217(α=0) = x Ln(x/b) + b – x Find: ZPoisson Z17(α=0) to pretty good accuracy |Z error| < .1 for x > 20

  7. Long Bursts • α =2.1o/cos(δ) / (30o - 2.1o/cos(δ) ) (T=2h) • Standard calculation • What happens if < 2h? • Not using Li Ma 17 for significance calculation • If I understand meaning of variables: • Seems to over-report significance by .3 - .5 • Probability too high by 3-10? • ZBinomial Z17 for long bursts—no strong need to change

  8. Long Burst Statistics Oct 03 to mid-Feb 04

  9. Why need to “recalibrate”? • Rate per year: needs • Correct probability for individual bursts • Correct trials • Live time needed to calculate them correctly • Trigger Mix dependent? • Oversampling • Is this optimized? • Correct interaction between time scales • Circular Issue Criteria Needed • Probability given short burst passes longer burst • Should be able to calculate burst by burst (x,b, then x’-x, b’-b) • Or maybe MC to calculate effective trials; or measure? • Will need time staring at David’s web pages (and Liz…) • I don’t see how the trigger rate enters very strongly • Enters in size of background estimate • Taken into account in probability calculation

  10. Queries • Is the P distribution flat? • Is its log-slope = -1? • If not, then probability calculation is wrong • Or complications with trials/oversampling…

  11. Comments • I still suspect that FDR would be a useful • Untriggered searches--some interesting papers: Jeff Scargle (NASA) at PHYSTAT 2003 Bruce Knuteson (HEP) at PHYSTAT 2003 & earlier • Both search for “best” regions (Varonni Tesselations) • Then calculate probability of such a fluctuation • An alternative to pre-determined trials choices • As usual, should study with MC the efficiency tradeoff • You can do better if you have a model • I will provide references • Minimize <limit>/typical signal? Billor paper?

  12. In Progress • Write this down, and circular criteria • Be sure understanding Liz’s “Off” variable • Understand Trials and Multiple time scales • Dump Long Burst database to Excel • Brenda asks: why flat in declination? • What drives it? • Solid angle? • Trials? (more 2h after all…)

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