CROSS-IDENTIFICATION OF SOURCES AND TRANSIENT EVENTS Tamás Budavári / The Johns Hopkins University 6/28/2011 

Tamás Budavári Multicolor Universe 6/28/2011 LOFAR Transients Key Project, Amsterdam 2 

Tamás Budavári Eventful Universe 6/28/2011 3 

Outline: matching detections in space and time Cross-Identification 4 6/28/2011 LOFAR Transients Key Project, Amsterdam 

Tamás Budavári What is the Right Question?  Cross-identification is a hard problem  Computationally, Scientifically & Statistically  Need symmetric n-way solution  Need reliable quality measure  Same or not?  Distance threshold? Maximum likelihood? 6/28/2011 5 LOFAR Transients Key Project, Amsterdam 

Tamás Budavári Modeling the Astrometry  Astrometric precision  A simple function  Where on the sky?  Anywhere really… 6/28/2011 6 LOFAR Transients Key Project, Amsterdam 

Tamás Budavári  The Bayes factor  H: all observations of the same object at m  K: might be from separate objects at {mi } Same or Not? 6/28/2011 7 LOFAR Transients Key Project, Amsterdam SAME NOT OR 

Tamás Budavári  The Bayes factor  H: all observations of the same object at m  K: might be from separate objects at {mi } Same or Not? On the sky Astrometry 6/28/2011 8 LOFAR Transients Key Project, Amsterdam SAME NOT OR 

Tamás Budavári  The Bayes factor  H: all observations of the same object at m  K: might be from separate objects at {mi } Same or Not? On the sky Astrometry 6/28/2011 9 LOFAR Transients Key Project, Amsterdam SAME NOT OR 

Tamás Budavári Normal Distribution  Astrometric precision  Fisher distribution  Analytic results cf. GRB repetition by Luo, Loredo & Wasserman (1996) 10 LOFAR Transients Key Project, Amsterdam 6/28/2011 

Tamás Budavári Normal Distribution  n-way  2-way TB & Szalay (2008) 11 LOFAR Transients Key Project, Amsterdam 6/28/2011 

6/28/2011 Same or not? Probability of a Match 12 LOFAR Transients Key Project, Amsterdam 

Tamás Budavári 6/28/2011 From Priors to Posteriors  Posterior probability from prior & Bayes factor  Prior probability of a match  Like dice in a bag: 1/N and N1n  In general? 13 LOFAR Transients Key Project, Amsterdam 

Tamás Budavári From Priors to Posteriors LOFAR Transients Key Project, Amsterdam 14  Different selections  Nearby / Distant  Red / Blue  But only 1 number 

Tamás Budavári  Prior has an unknown fudge-factor  Educated guess  Or solve for it: Self-Consistent Estimates TB & Szalay (2008) 6/28/2011 15 LOFAR Transients Key Project, Amsterdam 

Tamás Budavári Matching Events 6/28/2011 LOFAR Transients Key Project, Amsterdam 16 (1) (2) (x)  Streams of events in time and space  E.g., thresholded peaks in signal-to-noise 

Tamás Budavári Matching Events 6/28/2011 LOFAR Transients Key Project, Amsterdam 17  Bayes factors multiply  Simply combine spatial and time constraints 

Tamás Budavári Matching Events  Likelihood in time  From modeling fluxes : e.g., LSST SN Ia  Uniform prior in time?  Over  Artificial scaling!  , 6/28/2011 18 TB (2011) 

Tamás Budavári Matching Events 6/28/2011 LOFAR Transients Key Project, Amsterdam 19  Prior also scales with :  Cancels in the posterior  Analytic for simple forms 

Tamás Budavári Summary 6/28/2011 20  Bayesian approach to cross-identification  Places former heuristics on a firm statistical basis  Enables us to properly include  Physics, geometry, etc…  Naturally extends to time-domain  Events, proper motion, lightcurves  Opens the door for next-generation methods 

Tamás Budavári 6/28/2011 21 LOFAR Transients Key Project, Amsterdam