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SPIE 2008 :: Observatory Operations :: 7016-23 :: 16:20 Wednesday 25 June 2008

How to handle calibration uncertainties in high-energy astrophysics
Vinay Kashyap


SPIE 2008 :: Observatory Operations :: 7016-23 :: 16:20 Wednesday 25 June 2008

How to handle calibration uncertainties in high-energy astrophysics
Vinay Kashyap
CHASC Astrostatistical Collaboration Chandra X-ray Center Smithsonian Astrophysical Observatory

H y u n s o o k L e e , A n e ta S ie m ig in o w s k a , J o n a th a n M c D o w e ll, A r n o ld R o ts , J e r e m y D r a k e , P e t e R a t z l a f f, Andreas Zezas, Doug Burke, R im a Iz e m, A la n n a C o n n o r s , David van Dyk, Taeyoung Park


bottom line

there is now a way to include calibration uncertainty in astrophysical data analysis in a flexible way for any instrument, mission, or detector.


Part I calibration uncertainty in data analysis Part II practical issues of storage, retrieval, flexibility


The three most important effects that affect data analysis

astrophysical model uncertainty statistical uncertainty (measurement error) calibration uncertainty (systematic error)


examples of calibration uncertainty


p o w e r - la w r e s id u a ls w ith c u r r e n t c a lib r a tio n


p o w e r - la w r e s id u a ls w ith 2 0 е c o n ta m in a tio n o v e r la y e r


g e n e r a l m o d e l o f H E A d a ta

(E,p,t) : photon energy, location, arrival time (E',p') : detector channel, chip location

S : astrophysical source model R : energy redistribution function (RMF) P : position redistribution function (PSF) A : effective area (ARF) M : predicted model counts


effect on model parameter uncertainty

Probability density




but how exactly?


MCMC


DATA

CALIBRATION

Draw parameters

Compute likelihood

Update parameters


DATA

CALIBRATION

Draw effective areas

Draw parameters

Compute likelihood

Update parameters




b u t w h e r e d o th e e ffe c ti v e a r e a s c o m e fr o m ?



P r i n c i p a l C o m p o n e n ts


new

nominal

bias

~N (0,1) eigenvalue

PCs residual

A = A0 + bias + components + residual

eigenvector


Part II practical issues of storage, retrieval, flexibility

A = A0 + bias + components + residual


A = A0 + bias + components + residual
store in same format as A0 e.g., SPECRESP case specific secondary FITS extension e.g., PCA1D SIMS POLY1D PCPC MULTISCALE




what have we got so far? · · · · · · · · · realistic error bars implemented in BLoCXS 500x speed up in analysis Sherpa on the way unified file format for use in XSPEC/Sherpa 100x drop in storage generalize to any instrument extendable to model lacunae roll your own


s u m m a ry
there are a number of steps between a calibration scientist saying "the error on the effective area is X% at energy Y" to then have it fold into a spectral model fit and inflate the error bars on the parameters, and we believe that we have connected the dots.


uncertainty in energy response


one more thing..


what's next?

unified file format implemented in XSPEC/Sherpa other schemes of dimensionality reduction RMFs: 2D PCA, within and between PCA PSFs: multiscale residuals


Data

{
}
Calibration