Type Ia SN Light Curve Inference: Hierarchical Models for Nearby SN - - PowerPoint PPT Presentation

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Type Ia SN Light Curve Inference: Hierarchical Models for Nearby SN - - PowerPoint PPT Presentation

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Type Ia SN Light Curve Inference: Hierarchical Models for Nearby SN in the Rest-Frame Near Infrared (+Optical) Kaisey Mandel Harvard-Smithsonian Center for Astrophysics 17 September 2009 Thursday, September 17, 2009 Outline Statistical

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Kaisey Mandel Harvard-Smithsonian Center for Astrophysics 17 September 2009

Type Ia SN Light Curve Inference: Hierarchical Models for Nearby SN in the Rest-Frame Near Infrared (+Optical)

Thursday, September 17, 2009

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SLIDE 2

Outline

  • Statistical Inference with SN Ia Light curves
  • Hierarchical Framework for Constructing

Probability Models for Observed Data

  • Describing Populations & Individuals
  • Statistical Computation with Hierarchical Models
  • BayeSN (MCMC/Gibbs Sampling)
  • Application to Nearby CfA NIR Data (PAIRITEL)

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Thursday, September 17, 2009

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For more details: Mandel, K. , W.M. Wood-Vasey, A.S. Friedman, R.P . Kirshner. Type Ia Supernova Light Curve Inference: Hierarchical Bayesian Analysis in the Near Infrared. 2009, ApJ, in press (October). preprint: arXiv:0908.0536

Collaborators:

  • W. Michael Wood-Vasey (University of Pittsburgh),

Andrew Friedman, Gautham Narayan, Malcolm Hicken, Pete Challis, Robert Kirshner CfA Supernova Group

Thursday, September 17, 2009

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Statistical Learning from SN Ia is a complex inference problem

  • Empirical statistical models are learned from the data
  • Several Sources of Randomness & Uncertainty
  • Photometric errors (Observational Noise)
  • “Intrinsic Variation” = Population Distribution of SN Ia
  • Variations in light curve shape over time, intrinsic

color and luminosity vs λ : intrinsic correlation structure of SN Ia observeables

  • Random Peculiar Velocities in Hubble Flow
  • Host Galaxy Dust: extinction and reddening.
  • How to incorporate this all into a coherent statistical

model?

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Thursday, September 17, 2009

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SLIDE 5

Advantages of Hierarchical Models

  • Coherently and simultaneously incorporate multiple sources of

randomness & uncertainty: express complex probability models

  • Hierarchically Model (Physical) Populations and Individuals

simultaneously: e.g. SN Ia and Dust

  • Can model both intrinsic variations/correlations in color/luminosity/

light curve shape and dust reddening and extinction for populations and individuals

  • Explore & Marginalize over posterior trade-offs/joint distributions
  • Get full probability distribution not just point estimates:
  • global, coherent quantification of uncertainties,
  • can compute complete marginalization over posterior uncertainties
  • Modularity: Can incorporate additional statistical structure to parts of

the global model & condition on additional information (e.g. host galaxy type/environment, dust laws)

Thursday, September 17, 2009

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SLIDE 6

Directed Acyclic Graph for SN Ia Inference with Hierarchical Modeling

AppLC #N AbsLC #N Av, Rv #N Dust Pop AbsLC Pop

µN

D1

z1

zN

DN

AbsLC #1 AppLC #1 Av, Rv #1 µ1

  • Intrinsic Randomness
  • Dust Extinction & Reddening
  • Peculiar Velocities
  • Measurement Error

“Training” - Learn about Populations

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Generative Model Global Joint Posterior Probability Density Conditional on all SN Data

Thursday, September 17, 2009

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SLIDE 7

Directed Acyclic Graph for SN Ia Inference:

Distance Prediction

7

zs

Ds µs AppLCs s = 1, . . . , NSN As

V , Rs V

AbsLCs Training Prediction Ap

V , Rp V

µp Dp AppLCp AbsLCp Dust Pop SN Ia AbsLC Pop

Thursday, September 17, 2009

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SLIDE 8

Statistical Computation with Hierarchical SN Ia Models: The BayeSN Algorithm

  • Strategy: Generate a

Markov Chain to sample global parameter space (populations & all individuals) using Gibbs Sampling => seek a global sol’n

  • Chain explores/samples

trade-offs/degeneracies in global parameter space for populations and individuals

10 10

1

10

2

10

3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 MCMC Chain Sample AV Dust Extinction 1 2 3

Multiple chains globally converge from random initial values

Thursday, September 17, 2009

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SLIDE 9

Practical Application of Hierarchical Model: NIR SN Ia

Why are NIR SN Ia interesting?

  • Host Galaxy Dust presents a major

systematic uncertainty in supernova cosmology inference

  • Dust extinction has significantly

reduced effect in NIR bands

  • NIR SN Ia are good standard candles

(Elias et al. 1985, Meikle 2000, Krisciunas, et al. 2004+, Wood-Vasey, et al. 2008, Mandel et al. 2009).

  • Observe in NIR!: PAIRITEL /CfA

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Thursday, September 17, 2009

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NIR Observations from PAIRITEL

Credit: Andrew Friedman

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Observe in NIR bands J (λ=1.2 μm) H (λ=1.6 μm) Ks (λ=2.2 μm)

Thursday, September 17, 2009

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Nearby SN Ia in the NIR: The Training Data

WV08 Data Set = PAIRITEL + Lit = 39 SN Ia in NIR Working on 40-60 more SNe (Andy Friedman)

Credit: Michael Wood-Vasey, Andrew Friedman

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Light-curve shape variations in NIR

  • Double-Peak light-curve

structure seen in JHK bands

  • Difficult to capture with
  • ne parameter
  • J-band LC Model captures

timescales and amplitudes

  • f late-time NIR light

curves (Mandel et al. 2009)

1 2 3

d / α = 1±0.3

Normalized Magnitude

r / β = 1±0.3

20 40 60 1 2 3

α = 1±0.3

Normalized Magnitude (T−TBmax) / (1+z)

20 40 60

β = 1±0.3

(T−TBmax) / (1+z)

−10 10 20 30 40 50 60 −0.5 0.5 1 1.5 2 2.5 3 3.5

Time Since TBmax J − J0

J (39 SNe Ia)

J−band FLIR Template Original Data Transformed Data

Thursday, September 17, 2009

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SN NIR Population Inference: Peak Absolute Magnitudes

−18.35 −18.15 0.05 0.1 0.15 0.2 0.25 0.3 σ (MX) µ(MJ)

J

µ(MJ) = −18.26 σ (MJ) = 0.17 −18.1 −17.9 µ(MH)

H

µ(MH) = −18.00 σ (MH) = 0.11 −18.35 −18.15 µ(MKs)

Ks

µ(MKs) = −18.24 σ (MKs) = 0.18

  • Marginal Estimate of

Population Variance in H-band (1.6 μm) is σ(MH) = 0.11± 0.03 mag

  • SN Ia in NIR are

excellent standard candles!

Marginal Distributions of SN Ia NIR Population characteristics

Mandel et al. 2009

Thursday, September 17, 2009

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Hubble Diagram with nearby NIR SN Ia

10

3

10

4

30 32 34 36 µ(resub) h = 0.72 σpec = 150 km/s 39 JHKs distance moduli 10

3

10

4

−0.5 0.5 Velocity [CMB+Virgo] (km/s) Residual Residual Err (cz > 2000 km/s) = 0.10

Hubble Residuals of Hierarchical NIR SN Ia Model Fit

Bootstrap Cross- Validation: To Estimate effect of finite sample size ~ 0.05 mag: Need larger sample (Friedman, Wood-Vasey)

Mandel et al. 2009

Thursday, September 17, 2009

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SLIDE 15

Preview: Optical+NIR Hierarchical Inference

10 10 20 30 40 50 60 6 8 10 12 14 16 18 20 22

B + 2

SN2006ax (CfA3+PTEL)

V R 2 I 4 J 7 H 9

TTBmax Apparent Magnitude

Dust Law Slope RV

1

NIR Extinction AH

SN2006ax

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

10 10 20 30 40 50 60 6 8 10 12 14 16 18 20 22

B + 2

SN2005eq (CfA3+PTEL)

V R 2 I 4 J 7 H 9

TTBmax Apparent Magnitude

Dust Law Slope RV

1

NIR Extinction AH

SN2005eq

0.1 0.2 0.3 0.4 0.5 0.6 0.05 0.1 0.15 0.2 0.25

PTEL+CfA3 Light-curves Marginal Posterior of Dust (Preliminary)

Thursday, September 17, 2009

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Summary

  • Hierarchical models are useful statistical constructions

for incorporating multiple levels of randomness affecting SN Ia inference and modeling physical populations coherently

  • BayeSN: an efficient MCMC/Gibbs Sampler for

computing hierarchical models conditional on SN data

  • NIR Light Curves give excellent distances less prone

to dust extinction

  • Use Optical with NIR to estimate dust and make Type

Ia SN better standard candles (work in progress!)

  • Rest-Frame NIR observations of SN Ia: consideration

for JDEM

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Thursday, September 17, 2009