Bayesian Template-Based Approach to Classifying SDSS-II Supernovae from 3-Year Survey Brian Connolly Photometric Supernova ID Workshop 3/16/12

Outline The Goal PSNID SDSS-II 3-year Supernova Survey Analysis Results Comments Conclusions

Goal “Use the 3 year SDSS-II survey as a test bed to identify photometric SN Ia candidates [using a Bayesian methodology] with realistic estimates of purity” (obtained by using spectroscopically confirmed Ia’s)

Plan Estimate purity and efficiency (FoM) with spectroscopic sample Type photometric sample assuming these estimates Results (e.g., see if we can do cosmology)

Motivation for Bayesian Approach  2 (Ia) simply deviation from Ia hypothesis Estimate p-values, tail probabilities, severely underestimate Type I error rate No alternative included (not true with other classical tests) No alternative exists in classical approach Gives you want you want (derived from logically consistent framework) Includes information about lesser fits vs Ronald Fischer Thomas Bayes

PSNID Simplest Template-Based Bayesian Classifier Directly sum over all templates for all parameters and all types to find

Evidences  2 includes uncertainties in the model (which give good  2 /dof for high S/N) Likelihoods

Priors Host-z: or flat Type Milky Way R V =3.1, SN R V =2.2 A V, T max,  Flat

Idea Kuznetsova and Connolly (2007) advocated using knowledge of P(Ia) in addition to best fit. Plot P(Ia) vs.  r, find region in spec confirmed sample that maximizes purity and efficiency in photometric sample

SDSS-II Three Year Supernova Survey Sept-Nov deg 2 region along celestial equator using 2.5m telescope ugriz 0.1<z<0.4 Cadence 4 days (average) >10,000 new variable and transients in differenced images Small number ID-ed as Ia’s PSNID and spec confirmed Largest uniform sample of SN candidates to date to study classification (3221 photometric candidates pass quality cuts, 2776 no spec observations) SPLIT SAMPLE INTO SPECTROSCOPICALLY CONFIRMED AND UNCONFIRMED

Templates Ia’s: Sako et al. (2008) CC: start with Nugent, Nugent et al. (2002), near SDSS light curves-II, D’Andrea et al. (2010) and choose those that maximize Ia purity (and efficiency) 24→8 CC templates

Spec. Confirmed Ia 2006jz, z=0.2 Marginalized A V and  distributions factor of 2 larger than w/ spec. redshift prior

Spec. Confirmed Ia 2005it, z=0.3 * Parameter estimation done with MCMC

Spectroscopically Confirmed Sample 508 SNIa 80 CC 202 AGN PSNID Analysis w/out Host Z PSNID Analysis w Host Z -5<t<5 one epoch >15 days S/N>5 in two gri bands One search season 367 SNIa 45 CC 83 AGN Candidates Small number of CC’s, account for this by comparing how galaxies targeted (have well defined selection criteria)

Cuts on Confirmed Sample (candidates near SDSS galaxy spectrum)

FoM (1) (2) (3) True Ia’s ID-ed as Ia’s True Ia’s after cuts (Contamination) Different for spec and photo sample

Results

Spectroscopically Unconfirmed Sample 3221 candidates 2776 no host-z 445 with host-z

Unconfirmed Sample 860 candidates 94% Purity 92% Efficiency  2 optimized for P(Ia)>0.9 Total Unconfirmed Sample

Toward a Hubble Diagram

Hubble Diagram

Comments

SN Challenge

pSNid II Template fitting Classification schemes –“Classical” –Color –Rising light curves –Sequential analysis Input: ascii, FITS, database Output: ascii

Software Package: pSNid II Does It All JPAS Study

Comments Reduced  2 taken with grain of salt Start cutting in parameter space giving up purely Bayesian framework (Kunz et al., loss functions, etc.) Can set purity and efficiency independently – SEQUENTIAL ANALYSIS METHODS Milton Friedman

Conclusions Described method of photometrically classifying a large SN sample with the help of a small spectroscopic subsample 1070 photometric SN Ia candidates from the SDSS-II SN Survey data 94% purity and 6% contamination Hubble diagram –Eliminating A V >1 eliminates problems M. Sako et al.m, The Astrophysical Journal, Volume 738, Issue 2, article id. 162 (2011).

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Tuning W to get Purity/Efficiency Correct in Photometric Sample Ia/CC ratio incorrect as Ia’s mag limited Choose a mag-limited sample of those SNe with galaxy spectra Take ratio of W=[P(Ia)>0.9]/[P(Ia)<0.1]