How robust are SN Ia data?
Caroline Heneka
Valerio Marra, Luca Amendola (ITP Heidelberg)arXiv:1310.8435
COB, 17 Jan 2014
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
SN Ia as cosmological probes - where to improve?
increasing number of SNe & large number of effects:
→ systematic errors start dominating the overall error→ in need of purely statistical analysis methods
which are able toI investigate systematic effectsI detect correlations
with the aim toI pin-point subsets of contaminated dataI search for astrophysical/cosmological information
How robust are SN Ia data? Caroline Heneka 2/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
What is robustness?
robustness = consistency among subsets
Is there any subset statistically incompatible with others?→ likelihood contours shift and change size
How robust are SN Ia data? Caroline Heneka 3/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Bayesian view of robustness
robustness = consistency among subsets
Is there any subset statistically incompatible with others?→ likelihood contours shift and change size
How robust are SN Ia data? Caroline Heneka 3/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Bayesian view of robustness
robustness = consistency among subsets
Is there any subset statistically incompatible with others?→ likelihood contours shift and change size
How robust are SN Ia data? Caroline Heneka 3/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Internal Robustness
Bayesian comparison of 2 hypothesis:one set of parameters⇔ two independent distributions
Bayes’ ratio:
Btot ,ind =E (d;MC)
E (d1;MC)E (d2;MS)
d = full set, subsets d1 and d2, with d1 + d2 = dindependent models MC and MS
Internal Robustness:
R ≡ logBtot ,ind
Amendola, Quartin, Marra (arXiv:1209.1897)
How robust are SN Ia data? Caroline Heneka 4/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Internal Robustness
Bayesian comparison of 2 hypothesis:one set of parameters⇔ two independent distributions
Bayes’ ratio:
Btot ,ind =E (d;MC)
E (d1;MC)E (d2;MS)
d = full set, subsets d1 and d2, with d1 + d2 = dindependent models MC and MS
Internal Robustness - Fisher:
R = R0 +12
log|F1||F2|
|F tot |−
12
(χ̂2
tot − χ̂21 − χ̂
2S
)Amendola, Quartin, Marra (arXiv:1209.1897)
How robust are SN Ia data? Caroline Heneka 4/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Internal Robustness probability distribution function(IR-PDF)
parametrization choice of observable & partitioning of data↓
evaluate R − value for each chosen partition↓
IR − PDF
complete scan of all subsets impossible→ IR-PDF will depend on chosen partitions!→ IR-PDF for mock catalogues to test significance
How robust are SN Ia data? Caroline Heneka 5/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Our partitioning (arXiv:1310.8435) of Union2.0/2.1
I angular separationI z-binningI survey-wiseI hemispheres
arXiv:1310.8435: Heneka, Marra, AmendolaHow robust are SN Ia data? Caroline Heneka 6/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Internal Robustness probability distribution function:separation sorted
→ agreement within 2σ!→ no significant effects depending on angular separation→ similar for z-binning and survey-wise analysis
arXiv:1310.8435: Heneka, Marra, AmendolaHow robust are SN Ia data? Caroline Heneka 7/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Hemispherical directions
single partition (Planck) (α, δ) Significance
Hemispherical asymmetry (270◦,66.6◦) 1.26σ
Dipole anisotropy (167◦,−7◦) 0.39σ
Quadrupole-octupolealignment (177.4◦,18.7◦) 0.35σ
Grid of hemispheres
Direction of lowestrobustness
(150◦,70◦) 2.20σ
arXiv:1310.8435: Heneka, Marra, Amendola
How robust are SN Ia data? Caroline Heneka 8/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Preliminary: analysis of distance modulus errors
analysis applicable to any observable!
0.2 0.4 0.6 0.8 1.0 1.2 1.4z
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polynomial model for errors, lognormal distribution for mocks
How robust are SN Ia data? Caroline Heneka 9/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Preliminary: distribution of minimal robustness values
analysis of errors for 105 random partitions
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preliminary
How robust are SN Ia data? Caroline Heneka 10/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Take-away
advantagesI no specific effect assumedI fully Bayesian approach
applicationI improve understanding of systematics and correlationsI find most probable systematics-contaminated data
futureI test dependencies on SN and host galaxy propertiesI applicable to other data than SNe
quite robust, but still room for improvement!
How robust are SN Ia data? Caroline Heneka 11/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Extra slide: Distance modulus errors
I systematic parametrization: m(z) =∑
i λi ∗ z i
I lognormal assumption for synthetic catalogues
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52 SN, z=0.6-0.8, Μ=0.27, Σ=0.15
How robust are SN Ia data? Caroline Heneka 11/11
SNe Ia as tools Bayes - Internal Robustness Method Results Outlook
Extra slide: Distribution of most and least robust SNe
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How robust are SN Ia data? Caroline Heneka 11/11
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