Документ взят из кэша поисковой машины. Адрес оригинального документа : http://hea-www.harvard.edu/tanagra/etc/vlk_ICHASC2012_simultaneous_events.pdf Дата изменения: Thu Jan 24 03:32:21 2013 Дата индексирования: Fri Feb 28 11:04:16 2014 Кодировка: Поисковые слова: rigel

Simultaneous Weak Events
a new temporal analysis project

Vinay Kashyap Harvard-Smithsonian Center for Astrophysics

ICHASC Workshop, Imperial College, London, 23 Aug 2012


Chandra HETGS+ACIS-S grating dispersed events



Flares on HD 189733 that seem to be tied to planetary phase

Pillitteri et al. 2012, Cool Stars 17


Procyon : is there any variability?


Limitations in current analyses
· Likelihoods are constructed with no regard to data order
· ignoring auto-regression and ICA/SCA · fluctuations in consecutive bins, or groups of like fluctuations require human intervention via residual analysis

· Coincidences cannot be evaluated nonparametrically in multiple data streams
· we are more likely to believe that something is real if a signal is seen simultaneously in independent data streams



Limitations in current analyses
· Likelihoods are constructed with no regard to data order
· ignoring auto-regression and ICA/SCA · fluctuations in consecutive bins, or groups of like fluctuations require human intervention via residual analysis

· Coincidences cannot be evaluated nonparametrically in multiple data streams
· we are more likely to believe that something is real if a signal is seen simultaneously in independent data streams








Simulation
· Generate 500 draws from N(0,1) · Find all fluctuations at >1,1.5,2,2.5,3 sigma · Repeat 100 times · During each repetition, check how often a similar fluctuation is coincident with original fluctuation · Compute average frequency of coincidence · Repeat 100 times · Compare coincidence frequency with nominal probability of seeing coadded fluctuations of same sizes


Type I Error: Fraction of fluctuations that exceed k

k

1 0.16 0.025 0.078 0.025

1.5 0.067 0.0045 0.017 0.0045

2 0.022 0.0005 0.002 0.0005

2.5 0.006 0.0004 0.00015 0.0005

3 0.0013 8 10-7 10-5 4 10-6

N()
< N()| N()>

N()+ N() N()^2


Procyon : is there any variability?


Procyon : is there any variability?


Not the first time someone has tried to figure this out.

Stetson & Welch 1993 Lehner et al. 2010


Stetson & Welch 1993, AJ 105, 1813

· · · ·

variability index for two simultaneous streams first compute variance-weighted means then compute for each stream compute variability index as sum of (1)* (2)


Lehner et al. 2010, PASP 122, 959
· Not the first time someone has tried to figure this out. · Lehner et al. constructed a rank-ordered p-value statistic
to find occultation events.

· p-value defined as p(Z > z = ­ln(( r ) / NpT)) · Optimized for occultation events with no large time-scale
trends in the intensities

· Requires that statistical noise is not large


Type I is (relatively) easy; Type II is not. Still can't deal with grouped fluctuations. Want to detect weak events in streams dominated by background and statistical noise.