We have constructed a comprehensive statistical model for Type Ia supernova ( SN Ia ) light curves spanning optical through near infrared ( NIR ) data .
A hierarchical framework coherently models multiple random and uncertain effects , including intrinsic supernova light curve covariances , dust extinction and reddening , and distances .
An improved BayeSN MCMC code computes probabilistic inferences for the hierarchical model by sampling the global probability density of parameters describing individual supernovae and the population .
We have applied this hierarchical model to optical and NIR data of 127 SN Ia from PAIRITEL , CfA3 , CSP , and the literature .
We find an apparent population correlation between the host galaxy extinction A _ { V } and the the ratio of total-to-selective dust absorption R _ { V } .
For SN with low dust extinction , A _ { V } \lesssim 0.4 , we find R _ { V } \approx 2.5 - 2.9 , while at high extinctions , A _ { V } \gtrsim 1 , low values of R _ { V } < 2 are favored .
The NIR luminosities are excellent standard candles and are less sensitive to dust extinction .
They exhibit low correlation with optical peak luminosities , and thus provide independent information on distances .
The combination of NIR and optical data constrains the dust extinction and improves the predictive precision of individual SN Ia distances by about 60 \% .
Using cross-validation , we estimate an rms distance modulus prediction error of 0.11 mag for SN with optical and NIR data versus 0.15 mag for SN with optical data alone .
Continued study of SN Ia in the NIR is important for improving their utility as precise and accurate cosmological distance indicators .