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!

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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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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