Marquez, M.J.

A new approach to the optimization of the extraction

of astrometric and photometric information from

multiwavelength images in cosmological fields

GREAT Workshop 104/20/23

UNEDEUMETSAT

Marquez, M.J.

1. Data Mining Needs: multiwavelength observations

2. Objective 1: preliminary labelling

2.1. Objective 1: candidates for isolated sources

3. Objective 2: the cross-matching problem

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

3.2. Objective 2: implementation of the astrometric iterative

cross-matching

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

inference

3.4. Objective 2: astrometric and photometric Bayes factors.GREAT Workshop

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Structure

04/20/23

Marquez, M.J.

Structure3.5. 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.GREAT Workshop

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Marquez, M.J.

Data Mining need: multiwavelength Observations

GREAT Workshop

404/20/23

IRAC

IRAC

FOCAS

FOCAS

Marquez, M.J.

Objectives

Objective 1: to label the sources.

Objective 2: to construct reliable sets

possible overlapping

Note: in the following we will use the term channel

to refer to an image obtained in a given passband.

GREAT Workshop

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FLAG

FLAG

Marquez, M.J.

Objective 1: preliminary labelling

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FITS Images CATALOGUESSextractorSextractor

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Marquez, M.J.

2.1. Objective 1: candidates for isolated sources

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Future evolution

Maximum margin hyperplane.

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SVM

SVM

Marquez, M.J.

3. Objective 2: the cross-matching problem

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• Identification of the same source across multiple wavelength observations.

• Bayesian astrometric cross matching based on Budavari and Szalay (ApJ, 679 , 2008).

• Two mutually exclusive hypothesis:• H: all positions correspond to a single source.• K: not all positions correspond to a single

source.

• H will be represented by a single position on the sky and K will be represented by different celestial coordinates.

• Hypothesis comparison based on the Bayes factor, implemented as an iterative process

04/20/23

Marquez, M.J.

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

• Bayes Factor as the ratio of the two following evidences:

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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.

04/20/23

Marquez, M.J.

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

matching• 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.

04/20/23

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Marquez, M.J.

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

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B0 = 5

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σ ≤ 0.2’’

Marquez, M.J.

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

• 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.

GREAT Workshop

1204/20/23

Marquez, M.J.

3.4. Objective 2: astrometric and photometric Bayes factors

• 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,

2010GREAT Workshop

1304/20/23

Marquez, M.J.

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

problem

• 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.

GREAT Workshop

1404/20/23

Marquez, M.J.

3.5.1. Objective 2: bayesian Inference for the consideration of non detection

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• Photometric information is taken into account through SED models.

• The detection probability depends directly on the spatial flux density. For simplicity we assume here a simple threshold on the integrated flux.

• Starting point: each of the n-tuples from the astrometric cross-matching implementation.

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Marquez, M.J.

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

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Hypothesis:•H1: all the fluxes gi correspond to the same source .

•K1: not all the fluxes gi correspond to the same source

η: parameters for modelling the SED

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

Marquez, M.J.

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

• Hypothesis K1 can be decomposed in all possible combinations of non detections.

• Resolution of the corresponding combinatory problem.

• One new sub-hypothesis is established per combination derived from the combinatory problem.

GREAT Workshop

1704/20/23

Marquez, M.J.

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

GREAT Workshop

1804/20/23

Marquez, M.J.

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

GREAT Workshop

1904/20/23

Marquez, M.J.

4. Conclusions and Future Lines of Work.

Main conclusions:The proposed framework allows for the identification of the

channels that produce a consistent SED.

The selection of prior probabilities has a strong influence on the

selected model.

Future lines of work derived from current

limitations:The consideration of more than one non detection per channel

deserves a specific study of the problem.

The boundaries derived from the voronoi tessellation can be

improved.

The consideration of real astrometric position as a mathematical

point implies limitations for the case of extended sources.GREAT Workshop

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Marquez, M.J.

Thank you for your attention

GREAT Workshop

2104/20/23