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Publié par | ludwig-maximilians-universitat_munchen |
Publié le | 01 janvier 2010 |
Nombre de lectures | 15 |
Langue | English |
Poids de l'ouvrage | 22 Mo |
Extrait
Background–Source separation
in astronomical images
with Bayesian Probability Theory
Fabrizia Guglielmetti
M¨unchen 2010Background–Source separation
in astronomical images
with Bayesian Probability Theory
Fabrizia Guglielmetti
Dissertation der Fakult¨at fur¨ Physik
der Ludwig–Maximilians–Universit¨at M¨ unchen
f¨ur den Grad des
Doctor rerum naturalium
vorgelegt von
Fabrizia Guglielmetti
aus Rivarolo Canavese (Torino) - Italien
M¨ unchen, November 2010Erstgutachter: Prof. Dr. Hans B¨ohringer
Zweitgutachter: Prof. Dr. Dr.h.c. Volker Dose
Tag der mundlic¨ hen Prufung:¨ 1. Februar 2011Contents
Acronyms 12
Abstract 15
Zusammenfassung 16
Summary 17
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Conventional source detection methods . . . . . . . . . . . . . . . . . . . . 6
1.3 Advanced source detection methods . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Source detection methods employing BPT . . . . . . . . . . . . . . 8
1.3.2 The novel method with BPT . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2TheBStechnique 1
2.1 Bayesian probability theory .......................... 1
2.1.1 Py axioms ....... 12
2.1.2 Bayes’ theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Marginalization rule . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.4 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.5 Model comparison, classification . . . . . . . . . . . . . . . . . . . . 17
2.1.6 Mixture model technique . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 The joint estimation of background and sources . . . . . . . . . . . . . . . 21
2.2.1 Two–component mixture model . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Thin–plate spline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.3 Estimation of the background and its uncertainties . . . . . . . . . 33
2.2.4 Determining the hyperparameters . . . . . . . . . . . . . . . . . . . 34
2.2.5 Probability of hypothesis B ...................... 35
2.3 Source characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406CONTES
3Reliabilityofdetections 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.1 Historical note on testing . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 P-values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 The Bayesian viewpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Significance testing with p–values . . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Comparing threshold settings for source reliability.............. 46
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Source characterization from simulated data 55
4.1 Simulations set–up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.1 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.2 Hyperparameter estimation . . . . . . . . . . . . . . . . . . . . . . 60
4.2.3 The components of the mixture model . . . . . . . . . . . . . . . . 61
4.2.4 Source probability maps ........................ 63
4.2.5 Comparison between estimated and simulated source parameters . . 64
4.2.6 False positives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.7 Choice of the prior pdf of the source signal . . . . . . . . . . . . . . 72
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5Verificationwithexistingalgorithms 75
5.1 Standard techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Sliding window technique and Maximum Likelihood . . . . . . . . . 76
5.1.2 Wavelet Transformation . . . . . . . . . . . . . . . . . . . . . . . . 78
5.1.3 Voronoi Tessellation and Percolation . . . . . . . . . . . . . . . . . 79
5.1.4 Growth Curve Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1.5 Summary of some standard techniques . . . . . . . . . . . . . . . . 82
5.2 Application of standard techniques to sky surveys . . . . . . . . . . . . . . 83
5.2.1 XMM–COSMOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2.2 XMM–LSS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.2.3 Analysis of mosaic of images with the BSS algorithm . . . . . . . . 85
5.3 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6Applicationtoobservationaldata:ROSATAll-SkySurvey 93
6.1 ROSAT PSPC Survey Mode data . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2.1 Background analysis with BSS and SASS techniques . . . . . . . . 97
6.2.2 Catalogue comparisons . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2.3 Robustness of the BSS technique . . . . . . . . . . . . . . . . . . . 114
6.2.4 Discovery of new celestial objects . . . . . . . . . . . . . . . . . . . 125
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Table of Contents 7
7Aplicationtoobservationaldata:ChandraDepFieldSouth 135
7.1 The CDF–S region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.2 Performance of the BSS algorithm on the CDF–S region . . . . . . . . . . 142
7.2.1 Products of the BSS technique . . . . . . . . . . . . . . . . . . . . . 143
7.2.2 Field edge detection . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2.3 Comparison on real sources . . . . . . . . . . . . . . . . . . . . . . 144
7.2.4 Clusters and groups of galaxies . . . . . . . . . . . . . . . . . . . . 170
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8Concludingremarks&Outlok 195
8.1 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
AInverse–Gammadistribution 19
A.1 Relation between inverse–Gamma and power–law distributions . . . . . . . 199
A.2 Derivation of the marginal Poisson likelihood . . . . . . . . . . . . . . . . . 200
BThesplinemodel 203
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
B.2 Interpolation in one dimension space . . . . . . . . . . . . . . . . . . . . . 204
B.3 Interpolation in two dimensions . . . . . . . . . . . . . . . . . . . . . . . . 206
B.4 Interpolation using TPSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
CMinimizationprocedureforthebackgroundmodel 21
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Bibliography 215
Acknowledgments 238
Publications 2418TableofCntsList of Figures
2.1 Flow chart for background–source separation algorithm . .......... 21
2.2 Techniques for the correlation of neighbouring pixels . . . . . . . . . . . . 24
2.3 Prior pdfs of the source signal . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Likelihood pdfs versus photon counts . . . . . . . . . . . . . . . . . . . . . 28
2.5 Likelihood pdfs for the mixture model . . . . . . . . . . . . . . . . . . . . 30
2.6 Example of thin–plate spline . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.7 Distribution functions versus photon counts . . . . . . . . . . . . . . . . . 36
2.8 Flow chart for source characterization algorithm . . . . . . . . . . . . . . . 39
3.1 Classic hypothesis testing versus Bayesian approach (I) . . . . . . . . . . . 51
3.2 Classic hypothesis testing versus Bayesian approach (II) . . . . . . . . . . 52
3.3 Bayesian source probability variationswithsourceintensitiesonthefield . 53
4.1 Simulated data with small background . . . . . . . . . . . . . . . . . . . . 56
4.2 Simulated data with intermediate background . . . . . . . . . . . . . . . . 57
4.3 Simulated data with large background . . . . . . . . . . . . . . . . . . . . 58
4.4 Posterior pdf for hyperparameters . . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Comparison of mixture model components on data . . . . . . . . . . . . . 62
4.6 Analysis of source probabilities variation at multiple scales ......... 62
4.7 Analysis of source features at multiple scales . . . . . . . . . . . . . . . . . 65
4.8 Graphical comparison between estimated and simulated sources . . . . . . 66
4.9 Relation between net source counts, scales and P ............ 67source
4.10 Relation between simulated and measured sources . . . . . . . . . . . . . . 70
4.11 Analysis summary on simulated data . . . . . . . . . . . . . . . . . . . . . 71
5.1 wavdetect on simulated data (I) . . . . . . . . . . . . . . . . . . . . . . 88
5.2 Contamination versus e!ciency on simulated data . . . . . . . . . . . . . . 89
5.3 wavdetect on simulated data (II) . . . . . . . . . . . . . . . . . . . . . . 91
5.4 wavdetect on simulated data (III) . . . . . . . . . . . . . . . . . . . . . 91
6.1 Analysis of ROSAT PSPC data: RS930625n00................ 98
6.2 Exposure, BSS a