  We present an analysis of a sample of 69 local obscured Swift/Burst Alert
Telescope active galactic nuclei (AGNs) with X-ray spectra from NuSTAR and
infrared (IR) spectral energy distributions from Herschel and WISE. We combine
this X-ray and IR phenomenological modeling and find a significant correlation
between reflected hard X-ray emission and IR AGN emission, with suggestive
indications that this correlation may be stronger than the one between
intrinsic hard X-ray and IR emissions. This relation between the IR and
reflected X-ray emission suggests that both are the result of the processing of
intrinsic emission from the corona and accretion disk by the same structure. We
explore the resulting implications on the underlying distribution of covering
fraction for all AGNs, by generating mock observables for the reflection
parameter and IR luminosity ratio using empirical relations found for the
covering fraction with each quantity. We find that the observed distributions
of the reflection parameter and IR-to-X-ray ratio are reproduced with broad
distributions centered around covering fractions of at least ~40%-50%, whereas
narrower distributions match our observations only when centered around
covering fractions of ~70%-80%. Our results are consistent with both
independent estimates of the covering fractions of individual objects and the
typical covering fraction obtained on the basis of obscured fractions for
samples of AGNs. These results suggest that the level of reprocessing in AGNs,
including X-ray reflection, is related in a relatively straightforward way to
the geometry of the obscuring material.
