A new approach to the optimization of the extraction of astrometric and photometric information from multiwavelength images in cosmological fields. UNED EUMETSAT. Structure. Data Mining Needs : m ultiwavelength observations Objective 1: preliminary labelling
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A new approach to the optimization of the extraction of astrometric and photometric information from multiwavelength images in cosmological fields
2.1. Objective 1: candidatesforisolatedsources
3. Objective 2: thecross-matchingproblem
3.1. Objective 2: theresolution of thecross-matchingproblem
3.2. Objective 2: implementation of theastrometriciterativecross-matching
3.3. Objective 2: addingphotometrytothecross-matchinginference
3.4. Objective 2: astrometric and photometricBayesfactors.
3.5. Objective 2: an extended framework for the cross-matching problem
3.5.1. Objective 2: bayesian Inference for the consideration of non detection
3.5.2. Objective 2: hypothesis of the bayesian inference for the extended framework
3.5.2. Objective 2: resolution of all possible combinations of non detection
3.5.3. Objective 2: generic formalism of the bayesian inference for the extended framework
3.5.4. Objective 2: example of the extended framework for the case of three catalogues.
4. Conclusions and Future Lines of Work.
Note: in thefollowingwewill use thetermchanneltorefertoanimageobtained in a givenpassband.
Maximum margin hyperplane.
D = data composed of the positions measured.
m = real position parametrized with a three dimensional normal vector.
Bayes Factor as the ratio of the two following evidences:
This method computes, for n catalogues in an iterative way, the overall Bayes Factor in every step assuming that all other subsequent catalogues will contribute sources at the best possible position.
It establishes a correspondence between each Bayes Factor and a distance cut-off.
B0 = 5
σ ≤ 0.2’’
The formalism introduced so far is obviously valid when using photometric information.
Budavari and Szalay (ApJ, 679 , 2008) have introduced a Bayesian framework to photometric measurements in various passbands.
In the simplest case a model can be parametrized by a discrete spectral type T, the redshift z and an overall scaling factor for the brightness α.
Similarly to the astrometric equations, the photometric Bayes factor is given by the ratio:
The Bayesian analysis is inherently recursive. A consequence of this is that the combined Bayes factor of the astromeric and photometric measurements is simply the product of the two.
Jakob Walcher, Brent Groves, Tamás Budavari and Daniel Dale, 2010
Using a Bayes factor that includes photometry, we can conclude that a n-tuple produces an inconsistent SED if the hypothesis K is more probable but once this conclusion is reached, the SED is weeded out.
We propose here a formalism by which we can select which measures of the SED are consistent and therefore an incomplete but useful SED is produced.
η: parameters for modelling the SED
Cn,1 ; Cn,2; Cn,3;...;Cn,n
Futurelines of workderivedfromcurrentlimitations: