Bayesian f lux reconstruction in one and two bands
This presentation is the property of its rightful owner.
Sponsored Links
1 / 14

Bayesian f lux reconstruction in one and two bands PowerPoint PPT Presentation


  • 86 Views
  • Uploaded on
  • Presentation posted in: General

Bayesian f lux reconstruction in one and two bands . Statistical Challenges in Modern Astronomy V – June 13, 2011 Eric R. Switzer (KICP).

Download Presentation

Bayesian f lux reconstruction in one and two bands

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Bayesian f lux reconstruction in one and two bands

Bayesian flux reconstruction in one and two bands

Statistical Challenges in Modern Astronomy V – June 13, 2011

Eric R. Switzer (KICP)

T. M. Crawford, E. R. Switzer, W. L. Holzapfel, C. L. Reichardt, D. P. Marrone, and J. D. Vieira, “A Method for Individual Source Brightness Estimation in Single- and Multi-band Data” ApJ, 718:513–521, July 2010.


Bayesian f lux reconstruction in one and two bands

Intrinsicallyfaintsources are much more probable than bright sources.

It is more likely that the observed flux is a dimmer source and a positive noise fluctuation:“deboost” the measured flux.


The source problem

The source problem

~1’ resolution, 1 deg.: normal galaxy is unresolved for z>0.05 (200 Mpc), “point sources”

SPT 2mm; J. Vieira

Goal: posterior parameters {xi, Si,υ} given d and prior information.


The source problem1

The source problem

SPT 2mm; J. Vieira

Apply a matched filter, measure the flux Sm, but:


The single band multi source posterior distribution

The single-band, multi-source posterior distribution

Goal:

Distinction here: posterior of the brightest individual source of flux in a resolution element.

Data model:

Measurement

Likelihood:

(Scheuer

1957)

Where:

Prior:

Or, P(Ssmax) P(S>Ssmax)


The two band problem

The two-band problem

Suggesting the posterior:

If background sources approximate a Gaussian distribution:

(For experiments where the Gaussian assumption is not accurate, the full PDF can be developed as a 2D version of the single-band argument.)

Optionally either Flux1, Flux2, or e.g. Flux1 and alpha.


The two band posterior

The two-band posterior

0.5σ

4.2σ

4.9σ


Deboosting in the flux plane

Deboosting in the flux plane


Deboosting in the flux plane1

Deboosting in the flux plane

Dust locus

Sync. locus

Region of large flux errors(not shown for simplicity)


Uses and extensions

Uses and extensions

  • Population counts, spectral energy distributions, categorized source catalogs

  • P(α > αd) > Pd

  • Method to determine population counts from the flux PDFs of the catalog.

  • A rigorous multi-band, multi-experiment counts method with appropriate prior information.

AGN-powered, synchrotron-dominated, falling spectrum (in frequency). Dust emission-dominated, rising spectrum.


Uses and extensions1

Uses and extensions

  • Population counts, spectral energy distributions, categorized source catalogs

  • P(α > αd) > Pd

  • Method to determine population counts from the flux PDFs of the catalog.

  • A rigorous multi-band, multi-experiment counts method with appropriate prior information.


Uses and extensions2

Uses and extensions

  • Population counts, spectral energy distributions, categorized source catalogs

  • P(α > αd) > Pd

  • Method to determine population counts from the flux PDFs of the catalog.

  • A rigorous multi-band, multi-experiment counts method with appropriate prior information.

Right way: P(D) – what is the PDF of underlying counts model parameters which explains the PDF of pixel fluxes?


References

References

  • This talk: T. M. Crawford, E. R. Switzer, W. L. Holzapfel, C. L. Reichardt, D. P. Marrone, and J. D. Vieira, “A Method for Individual Source Brightness Estimation in Single- and Multi-band Data,” ApJ, 718:513–521, July 2010.

  • Bayesian catalogs: P. Carvalho, G.Rocha, and M. P. Hobson, “A fast Bayesian approach to discrete object detection in astronomical data sets - PowellSnakesI,” MNRAS, 393:681–702, March 2009.

  • P(D) method:Patanchonet al., “Submillimeter Number Counts from Statistical Analysis of BLAST Maps,” ApJ, 707:1750–1765, December 2009.

  • PDF of source fluxes: P. A. G. Scheuer, “A statistical method for analysing observations of faint radio stars,” In Proceedings of the Cambridge Philosophical Society, volume 53 pages 764–773, 1957.

  • Method here applied to SPT data: J. D. Vieira, T. M. Crawford, E. R. Switzer, et al. “Extragalactic Millimeter-wave Sources in South Pole Telescope Survey Data: Source Counts, Catalog, and Statistics for an 87 Square- degree Field,” ApJ, 719:763–783, August 2010.

  • Deboosting in literature: K. Coppin, M. Halpern, D. Scott, C. Borys, and S. Chapman, “An 850-μm SCUBA map of the Groth Strip and reliable source extraction” MNRAS, 357:1022–1028, March 2005.

  • https://github.com/eric-switzer/bayes_flux


  • Login