A new approach to the optimization of the extraction of astrometric and photometric information from...
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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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Uned eumetsat

A new approach to the optimization of the extraction of astrometric and photometric information from multiwavelength images in cosmological fields

UNED

EUMETSAT

GREAT Workshop


Structure

Structure

GREAT Workshop

  • Data MiningNeeds: multiwavelengthobservations

  • Objective 1: preliminarylabelling

    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.


Structure1

Structure

GREAT Workshop

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.


Data m ining need m ultiwavelength observations

Data Miningneed: multiwavelengthObservations

IRAC

FOCAS

GREAT Workshop


Objectives

Objectives

FLAG

GREAT Workshop

  • Objective 1: tolabelthesources.

  • Objective 2: toconstructreliable sets

    possibleoverlapping

    Note: in thefollowingwewill use thetermchanneltorefertoanimageobtained in a givenpassband.


Objective 1 preliminary labelling

Objective 1: preliminary labelling

  • FITS Images CATALOGUES

Sextractor

GREAT Workshop


2 1 objective 1 candidates for isolated sources

2.1. Objective 1: candidates for isolated sources

Future evolution

SVM

Maximum margin hyperplane.

GREAT Workshop


3 objective 2 the cross matching problem

3. Objective 2: the cross-matching problem

  • Identification of thesamesourceacrossmultiplewavelengthobservations.

  • BayesianastrometriccrossmatchingbasedonBudavari and Szalay (ApJ, 679 , 2008).

  • Twomutually exclusive hypothesis:

    • H: all positions correspondto a single source.

    • K: notall positions correspondto a single source.

  • H will be representedby a single position onthesky and K will be representedbydifferent celestial coordinates.

  • HypothesiscomparisonbasedontheBayes factor, implemented as aniterativeprocess

GREAT Workshop


3 1 objective 2 the resolution of the cross matching problem

3.1. Objective 2: the resolution of the cross-matching problem

  • p(m|H): probability that the source is in the position m.

  • p(xi|m,H): probability that one source of channel i which is in the position m is detected in the position xi

D = data composed of the positions measured.

m = real position parametrized with a three dimensional normal vector.

GREAT Workshop

Bayes Factor as the ratio of the two following evidences:


3 2 objective 2 implementation of the astrometric iterative cross matching

3.2. Objective 2: implementation of the astrometric iterative cross-matching

GREAT Workshop

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.


3 2 objective 2 implementation of the astrometric iterative cross matching1

3.2. Objective 2: implementation of the astrometric iterative cross-matching

B0 = 5

σ ≤ 0.2’’

GREAT Workshop


3 3 objective 2 adding photometry to the cross matching inference

3.3. Objective 2: adding photometry to the cross-matching inference

GREAT Workshop

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.


3 4 objective 2 astrometric and photometric bayes factors

3.4. Objective 2: astrometric and photometric Bayes factors

GREAT Workshop

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


3 5 objective 2 an extended framework for the cross matching problem

3.5. Objective 2: an extended framework for the cross-matching problem

GREAT Workshop

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.


3 5 1 objective 2 bayesian inference for the consideration of non detection

3.5.1. Objective 2: bayesianInferencefortheconsideration of non detection

  • Photometricinformationistakenintoaccountthrough SED models.

  • Thedetectionprobabilitydependsdirectlyonthespatial flux density. Forsimplicityweassumehere a simple thresholdontheintegrated flux.

  • Startingpoint: each of the n-tuplesfromtheastrometriccross-matchingimplementation.

GREAT Workshop


3 5 2 objective 2 hypothesis of the bayesian inference for the extended framework

3.5.2. Objective 2: hypothesis of the bayesian inference for the extended framework

η: parameters for modelling the SED

  • Hypothesis:

  • H1: allthefluxesgicorrespondtothesamesource .

  • K1: notallthefluxesgicorrespondtothesamesource

Cn,1 ; Cn,2; Cn,3;...;Cn,n

GREAT Workshop


Uned eumetsat

  • 3.5.3. Objective 2: generic formalism of the bayesian inference for the extended framework

  • Hypothesis K1 can be decomposed in allpossiblecombinations of non detections.

  • Resolution of thecorrespondingcombinatoryproblem.

  • One new sub-hypothesisisestablished per combinationderivedfromthecombinatoryproblem.

GREAT Workshop


Uned eumetsat

  • 3.5.3. Objective 2: generic formalism of the bayesian inference for the extended framework

GREAT Workshop


3 5 4 objective 2 example of the extended framework for the case of three catalogues

3.5.4. Objective 2: example of the extended framework for the case of three catalogues.

GREAT Workshop


4 conclusions and future lines of work

4. Conclusions and Future Lines of Work.

GREAT Workshop

Mainconclusions:

  • Theproposedframeworkallowsfortheidentification of thechannelsthat produce a consistent SED.

  • Theselection of prior probabilities has a stronginfluenceontheselectedmodel.

    Futurelines of workderivedfromcurrentlimitations:

  • Theconsideration of more thanone non detection per channeldeserves a specificstudy of theproblem.

  • Theboundariesderivedfromthevoronoitessellation can be improved.

  • Theconsideration of real astrometric position as a mathematicalpointimplieslimitationsforthe case of extended sources.


Thank you for your attention

Thank you for your attention

GREAT Workshop


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