Cosmological parameter estimation techniques that robustly account for systematic measurement uncertainties will be crucial for the next generation of cosmological surveys .
We present a new analysis method , superABC , for obtaining cosmological constraints from Type Ia supernova ( SN Ia ) light curves using Approximate Bayesian Computation ( ABC ) without any likelihood assumptions .
The ABC method works by using a forward model simulation of the data where systematic uncertainties can be simulated and marginalized over .
A key feature of the method presented here is the use of two distinct metrics , the ‘ Tripp ’ and ‘ Light Curve ’ metrics , which allow us to compare the simulated data to the observed data set without likelihood assumptions .
The Tripp metric takes as input the parameters of models fit to each light curve with the SALT-II method , whereas the Light Curve metric uses the measured fluxes directly without reference to model fitting .
We apply the superABC sampler to a simulated data set of \sim 1000 SNe corresponding to the first season of the Dark Energy Survey Supernova Program ( DES-SN ) .
We investigate the effect of systematic uncertainties on parameter constraints from the ABC sampler by including 1 % calibration uncertainties .
Varying five parameters , \Omega _ { m } ,w _ { 0 } , \alpha and \beta and a magnitude offset parameter , with a CMB prior and no systematics we obtain \Delta ( w _ { 0 } ) = w _ { 0 } ^ { true } - w _ { 0 } ^ { best fit } = -0.036 \pm 0.109 ( a \sim 11 % 1 \sigma uncertainty ) using the Tripp metric and \Delta ( w _ { 0 } ) = -0.055 \pm 0.068 ( a \sim 7 % 1 \sigma uncertainty ) using the Light Curve metric .
Including calibration uncertainties in four passbands , adding 4 more parameters ( 9 total ) , we obtain \Delta ( w _ { 0 } ) = -0.062 \pm 0.132 ( a \sim 14 % 1 \sigma uncertainty ) using the Tripp metric .
Overall we find a 17 % increase in the uncertainty on w _ { 0 } with systematics compared to without .
We contrast this with a MCMC approach where systematic effects are approximately included as a fixed uncertainty in the covariance matrix .
We find that the MCMC method slightly underestimates the impact of calibration uncertainties for this simulated data set .