  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 <
0.4, we find R_V = 2.5 - 2.9, while at high extinctions, A_V > 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.
